(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[         0,          0]
NotebookDataLength[    190633,       6096]
NotebookOptionsPosition[    176758,       5833]
NotebookOutlinePosition[    177246,       5853]
CellTagsIndexPosition[    177203,       5850]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Global definitions", "Section",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, 
   3.760632508859365*^9, {3.760679169140106*^9, 3.7606791775879383`*^9}, {
   3.782223108642475*^9, 
   3.782223110395791*^9}},ExpressionUUID->"14656a38-3554-4a83-a92b-\
19dd9f26f677"],

Cell[CellGroupData[{

Cell["Fundamental unit w of Q[\\sqrt{5}]", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.76063016392813*^9, 
   3.760630165007289*^9}, {3.760632526560926*^9, 3.760632544154763*^9}, 
   3.7606344015819817`*^9, {3.760679231369814*^9, 3.760679242922057*^9}, {
   3.760679346800742*^9, 3.7606793469949207`*^9}, {3.761122318129079*^9, 
   3.761122319769112*^9}},ExpressionUUID->"ba38d90f-9f56-4c32-ab1a-\
2c10dd50fb99"],

Cell[BoxData[
 RowBox[{
  RowBox[{"w", "=", 
   FractionBox[
    RowBox[{"1", "+", 
     RowBox[{"Sqrt", "[", "5", "]"}]}], "2"]}], ";"}]], "Input",
 CellChangeTimes->{{3.780675396915119*^9, 3.7806754009103527`*^9}},
 CellLabel->
  "In[119]:=",ExpressionUUID->"523e1b05-8bc2-42dc-9699-1ee01a010fe5"]
}, Closed]],

Cell[CellGroupData[{

Cell["Its symbolic counterpart W", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.76063016392813*^9, 
   3.760630165007289*^9}, {3.760632526560926*^9, 3.760632544154763*^9}, 
   3.7606344015819817`*^9, {3.760679249706262*^9, 3.760679259845272*^9}, {
   3.760679349426751*^9, 3.760679349830819*^9}, {3.7627489253354263`*^9, 
   3.762748926552051*^9}},ExpressionUUID->"e34f0406-b25e-4c04-be88-\
09fbbd2bc598"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Clear", "[", "W", "]"}], ";"}]], "Input",
 CellChangeTimes->{{3.760679214674675*^9, 3.760679219002922*^9}},
 CellLabel->
  "In[120]:=",ExpressionUUID->"9f07e933-6f88-438b-a93c-aa55e066714c"]
}, Closed]],

Cell[CellGroupData[{

Cell["Bringing entries of a matrix to the canonical form a + b W", \
"Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.76063016392813*^9, 
   3.760630165007289*^9}, {3.760632526560926*^9, 3.760632544154763*^9}, 
   3.7606344015819817`*^9, {3.760679249706262*^9, 3.760679259845272*^9}, {
   3.7606793059838247`*^9, 
   3.760679339404605*^9}},ExpressionUUID->"58d1b469-9b5a-4f36-a092-\
13feb4807ed2"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"Canonize", "[", "x_", "]"}], " ", ":=", " ", 
   RowBox[{"Switch", "[", 
    RowBox[{
     RowBox[{"Length", "[", 
      RowBox[{"ToNumberField", "[", 
       RowBox[{"x", ",", "w"}], "]"}], "]"}], ",", "0", ",", "x", ",", "2", 
     ",", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"ToNumberField", "[", 
         RowBox[{"x", ",", "w"}], "]"}], "[", 
        RowBox[{"[", "2", "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", "+", " ", 
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{"ToNumberField", "[", 
          RowBox[{"x", ",", "w"}], "]"}], "[", 
         RowBox[{"[", "2", "]"}], "]"}], "[", 
        RowBox[{"[", "2", "]"}], "]"}], " ", "W"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"SetAttributes", "[", 
   RowBox[{"Canonize", ",", " ", "Listable"}], "]"}], ";"}]}], "Input",
 CellChangeTimes->{{3.76063380011486*^9, 3.760633819602181*^9}, {
  3.7606338673889008`*^9, 3.7606338674385653`*^9}, {3.760633913027965*^9, 
  3.760633925495439*^9}, {3.760679360709139*^9, 3.760679361562168*^9}, {
  3.762427611308568*^9, 3.762427645382559*^9}},
 CellLabel->
  "In[121]:=",ExpressionUUID->"0b6880d5-4523-48e5-b931-301e9c803020"]
}, Closed]],

Cell[CellGroupData[{

Cell["Reducing a number field x element modulo ideal I=(y)", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.76063016392813*^9, 
   3.760630165007289*^9}, {3.760632526560926*^9, 3.760632544154763*^9}, 
   3.7606344015819817`*^9, {3.760679249706262*^9, 3.760679259845272*^9}, {
   3.7606793059838247`*^9, 3.760679339404605*^9}, {3.7725539486937933`*^9, 
   3.772553971318605*^9}},ExpressionUUID->"9a31f9b5-514c-41e1-84a7-\
0ac90acebfa7"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"NumberFieldElementReduction", "[", 
    RowBox[{"x_", ",", "y_"}], "]"}], ":=", 
   RowBox[{"PolynomialMod", "[", 
    RowBox[{"x", ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{
        RowBox[{"W", "^", "2"}], "-", "W", "-", "1"}], ",", "y"}], "}"}]}], 
    "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"SetAttributes", "[", 
   RowBox[{"NumberFieldElementReduction", ",", "Listable"}], "]"}], 
  ";"}]}], "Input",
 CellChangeTimes->{{3.762429417106452*^9, 3.762429482043982*^9}, {
  3.7624296173551064`*^9, 3.76242970100613*^9}, {3.762709013464142*^9, 
  3.762709017224141*^9}},
 CellLabel->
  "In[123]:=",ExpressionUUID->"bc731114-24c1-40b7-8ac2-67b8dedbc24a"]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Computing the order of a matrix m with entries in the field reduced modulo \
ideal I=(p)\
\>", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.76063016392813*^9, 
   3.760630165007289*^9}, {3.760632526560926*^9, 3.760632544154763*^9}, 
   3.7606344015819817`*^9, {3.760679249706262*^9, 3.760679259845272*^9}, {
   3.7606793059838247`*^9, 3.760679339404605*^9}, {3.772553980849586*^9, 
   3.772554013019011*^9}},ExpressionUUID->"8e02da97-769b-4a13-b665-\
f98fee9a0bdb"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"MatrixReductionOrder", "[", 
    RowBox[{"m_", ",", "p_", ",", 
     RowBox[{"maxOrder_:", " ", 
      RowBox[{"10", "^", "10"}]}]}], "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"n", "=", "1"}], ",", 
       RowBox[{"id", "=", 
        RowBox[{"IdentityMatrix", "[", 
         RowBox[{"Length", "[", "m", "]"}], "]"}]}]}], "}"}], ",", 
     RowBox[{
      RowBox[{"NestWhile", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"n", "++"}], ";", 
           RowBox[{"NumberFieldElementReduction", "[", 
            RowBox[{
             RowBox[{"m", ".", "#"}], ",", "p"}], "]"}]}], ")"}], "&"}], ",", 
        RowBox[{"NumberFieldElementReduction", "[", 
         RowBox[{"m", ",", "p"}], "]"}], ",", 
        RowBox[{
         RowBox[{"!", 
          RowBox[{"And", "@@", 
           RowBox[{"(", 
            RowBox[{"PossibleZeroQ", "/@", 
             RowBox[{"Flatten", "[", 
              RowBox[{"#", "-", "id"}], "]"}]}], ")"}]}]}], "&"}], ",", "1", 
        ",", "maxOrder"}], "]"}], ";", "n"}]}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.762428455725996*^9, 3.7624285047629557`*^9}, {
  3.762428944982642*^9, 3.7624289472156982`*^9}, {3.762429038247916*^9, 
  3.7624290436705027`*^9}, {3.7624291423465776`*^9, 3.76242918452512*^9}, {
  3.76242976434914*^9, 3.762429802254305*^9}},
 CellLabel->
  "In[125]:=",ExpressionUUID->"e3862526-5b9f-4a42-8dc3-dbdd97875f95"]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Polytope P_5", "Section",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.76063016392813*^9, 
   3.760630165007289*^9}, {3.760632526560926*^9, 3.760632544154763*^9}, 
   3.7606344015819817`*^9, {3.760634613106736*^9, 3.760634616976028*^9}, {
   3.7646053060631847`*^9, 3.764605333357589*^9}, {3.7806738519931097`*^9, 
   3.7806738527716208`*^9}},ExpressionUUID->"4fe39d2d-a7ae-47be-adfb-\
2dbc19ef7abc"],

Cell[CellGroupData[{

Cell["Quadratic form associated to polytope P_5 in H^5", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.76063016392813*^9, 
   3.760630165007289*^9}, {3.760632526560926*^9, 3.760632544154763*^9}, 
   3.7606344015819817`*^9, {3.7646053197548513`*^9, 
   3.7646053210482273`*^9}},ExpressionUUID->"586cf5a7-92da-4e89-8aad-\
2a8dbfa9eab8"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"q5", "[", 
    RowBox[{"{", 
     RowBox[{
     "x0_", ",", "x1_", ",", "x2_", ",", "x3_", ",", "x4_", ",", "x5_"}], 
     "}"}], "]"}], "=", 
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", 
        RowBox[{"2", "w"}]}], ")"}]}], " ", 
     SuperscriptBox["x0", "2"]}], "+", 
    SuperscriptBox["x1", "2"], "+", 
    SuperscriptBox["x2", "2"], "+", 
    SuperscriptBox["x3", "2"], "+", 
    SuperscriptBox["x4", "2"], "+", 
    SuperscriptBox["x5", "2"]}]}], ";"}]], "Input",
 CellChangeTimes->{{3.75833102477936*^9, 3.758331038483093*^9}, {
  3.758331108311313*^9, 3.758331114658369*^9}, {3.7583341660018034`*^9, 
  3.758334169783081*^9}, {3.7583346817301817`*^9, 3.7583346915199986`*^9}, {
  3.758334955891484*^9, 3.7583349570170317`*^9}, {3.7583351720451264`*^9, 
  3.758335174690775*^9}, {3.7583352241967697`*^9, 3.7583352249319587`*^9}, {
  3.7583358468129377`*^9, 3.7583358486468563`*^9}, {3.758479404237545*^9, 
  3.7584794214592595`*^9}, {3.7584823877991977`*^9, 3.758482393962841*^9}, {
  3.761122412284438*^9, 3.761122489627466*^9}, {3.761122537856392*^9, 
  3.761122539260841*^9}, {3.76112262761552*^9, 3.761122628487047*^9}, {
  3.762878880936632*^9, 3.762878881579831*^9}},
 CellLabel->
  "In[126]:=",ExpressionUUID->"6b64ac43-4543-44e4-b995-6564add16920"]
}, Closed]],

Cell[CellGroupData[{

Cell["Standard basis of R^{1,5}", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
  3.760629982671979*^9, 3.760629990092085*^9}, {3.760630037438387*^9, 
  3.760630046659821*^9}},ExpressionUUID->"caa59798-9eb5-4c6f-84bf-\
6e76f6475984"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{"v0", ",", "v1", ",", "v2", ",", "v3", ",", "v4", ",", "v5"}], 
    "}"}], "=", 
   RowBox[{"IdentityMatrix", "[", "6", "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.741986259869416*^9, 3.7419862881029577`*^9}, {
  3.753271317323329*^9, 3.753271354773836*^9}, {3.754247538035009*^9, 
  3.7542475546382313`*^9}, {3.7542655074583955`*^9, 3.754265525374155*^9}, {
  3.7583347561999874`*^9, 3.7583347762341795`*^9}, {3.758479559595871*^9, 
  3.758479574630477*^9}, {3.762938115325974*^9, 3.762938151874105*^9}},
 CellLabel->
  "In[127]:=",ExpressionUUID->"50a66ac0-62f9-4740-9d9d-ba0add622f50"]
}, Closed]],

Cell[CellGroupData[{

Cell["Reflection associated to a given root", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
  3.760629982671979*^9, 3.760629990092085*^9}, {3.7606300544805603`*^9, 
  3.7606300665456867`*^9}},ExpressionUUID->"0240d1ab-7609-44f6-84ae-\
bbc687460272"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Ref", "[", 
    RowBox[{"{", 
     RowBox[{
     "x0_", ",", "x1_", ",", "x2_", ",", "x3_", ",", "x4_", ",", "x5_"}], 
     "}"}], "]"}], "=", 
   RowBox[{"Join", "[", 
    RowBox[{
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v0", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{"-", "1"}], "+", 
                RowBox[{"2", "w"}]}], ")"}]}], " ", " ", "x0"}], ")"}]}], 
          RowBox[{"q5", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
            "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
          "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v1", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x1"}], 
          RowBox[{"q5", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
            "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
          "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v2", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x2"}], 
          RowBox[{"q5", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
            "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
          "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v3", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x3"}], 
          RowBox[{"q5", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
            "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
          "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v4", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x4"}], 
          RowBox[{"q5", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
            "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
          "}"}]}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v5", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x5"}], 
          RowBox[{"q5", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
            "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5"}], 
          "}"}]}]}], "}"}], "]"}], ",", "2"}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->CompressedData["
1:eJxTTMoPSmViYGAQA2IQnT/5xDrXh68d8x6zbgDRflr7T4No7c9nwPS1yfl3
QLTXt+WvQDTf4pnvQPQ3k9KPIHr7UvP/IDpa9gCLG5AWufBEBERn/FGSBNG5
C/gUQXTKAhElEG31arU+iL6/YJIBiNbbdC0bRDct3J0PoqeU5Buf+QakRTrA
9KNcBksQvabvNZjmSVl4E0TPSGx5BaKfBGrznwXSZVq2YNqjK3fjih+vHZmu
79sKouP4o8o3AulDAvdrQfSSfz/TSxjeOE4pWJ8HouPa+apBtHSuHpjWmlDZ
AaL14sz6QfTsnbvXg+gPQl/B9LQ7btK7gXTFoQYFEK3S2+8IokOWbQTTD/Z2
VO8B0uXiT2pANADZ273O
  "],
 CellLabel->
  "In[128]:=",ExpressionUUID->"3d591a9f-e348-4576-b0b4-7bc2099d449c"]
}, Closed]],

Cell[CellGroupData[{

Cell["Outer normals for P_5 determined by Vinberg\[CloseCurlyQuote]s \
algorithm", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
  3.760629982671979*^9, 3.760629990092085*^9}, {3.760630081373625*^9, 
  3.760630103352571*^9}},ExpressionUUID->"242f1bf9-b52c-454f-a26c-\
f6c70bf4069e"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"e1", "=", 
    RowBox[{
     RowBox[{"-", "v1"}], "+", "v2"}]}], ";"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e2", "=", 
   RowBox[{
    RowBox[{"-", "v2"}], "+", "v3"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e3", "=", 
   RowBox[{
    RowBox[{"-", "v3"}], "+", "v4"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e4", "=", 
   RowBox[{
    RowBox[{"-", "v4"}], "+", "v5"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e5", "=", 
   RowBox[{"-", "v5"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e6", "=", 
   RowBox[{
    RowBox[{"w", " ", "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", "w"}], ")"}], "v1"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e7", "=", 
   RowBox[{"w", 
    RowBox[{"(", 
     RowBox[{"v0", "+", "v1", "+", "v2", "+", "v3"}], ")"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e8", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", "w"}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v0", "+", "v1"}], ")"}]}], "+", 
    RowBox[{"w", 
     RowBox[{"(", 
      RowBox[{"v2", "+", "v3", "+", "v4", "+", "v5"}], ")"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e9", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"6", "+", 
       RowBox[{"9", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"4", "+", 
       RowBox[{"7", "w"}]}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v1", "+", "v2", "+", "v3", "+", "v4"}], ")"}]}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", "w"}], ")"}], "v5"}]}]}], ";"}]}], "Input",
 CellChangeTimes->CompressedData["
1:eJwdxU8oQ3EAB/BnxAU50PNnraZsxhJSasp6RRxMy5IbwlbI1CYtB20rf1qs
1CZtkqLXxAEbipI/K3+yDWU1l2WlpXFQmzb14n1/h08f8dBkj1ZAUZSQh9VG
37EnnWBagvdn2M8NXGJamyarIsu32O0uvMMxy9TsAf/M0aMZ07nmsqpMgqnf
fyvHleMatYzfucKS41zFOb5WtpK39ZJkDX+WS5TCoo2GDG7T+Mjr37LjDn4J
NXKCfxZXr7BCr/Lj1CsbwCrvaxA7uksMU9Qn49hpmsbep+raaf7fCCfHS/PZ
zVgnGCU/yN+V2MK2M1gfnxvGedbwCN5ThCZwWhonh21iIzY5I2RHwGrC+XY7
+Tm8a8GHvUny9+CCDXe5aSfuLzVwWFjt+cNjdPTExS9b9JziEu3NBWYLpJe4
r3grhHWznU84WvclPuPf/Ig14rW8gPwl55PxuIrq8D9Xhufh
  "],
 CellLabel->
  "In[129]:=",ExpressionUUID->"1f1ee5de-24f9-47f0-a0e9-29be6458ba84"]
}, Closed]],

Cell[CellGroupData[{

Cell["Reflections in the bounding hyperplanes of P_5", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
  3.760629982671979*^9, 3.760629990092085*^9}, {3.760630171933566*^9, 
  3.760630181461022*^9}},ExpressionUUID->"2ff5c21b-63ac-45d6-a0f5-\
f0dd525ead4b"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"s1", "=", 
   RowBox[{"Ref", "[", "e1", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s2", "=", 
   RowBox[{"Ref", "[", "e2", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s3", "=", 
   RowBox[{"Ref", "[", "e3", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s4", "=", 
   RowBox[{"Ref", "[", "e4", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s5", "=", 
   RowBox[{"Ref", "[", "e5", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s6", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e6", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s7", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e7", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s8", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e8", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s9", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e9", "]"}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.7583349010431814`*^9, 3.7583349033210793`*^9}, {
  3.7583349411761537`*^9, 3.7583349412939816`*^9}, {3.758335374359543*^9, 
  3.758335432323221*^9}, {3.75834115524435*^9, 3.7583411844974585`*^9}, {
  3.758413279687951*^9, 3.7584132884369483`*^9}, {3.758413462371809*^9, 
  3.7584134717453995`*^9}, {3.758479773657228*^9, 3.7584797822090273`*^9}, {
  3.760630209482951*^9, 3.760630218833775*^9}, {3.760630349926944*^9, 
  3.760630361264076*^9}},
 CellLabel->
  "In[138]:=",ExpressionUUID->"c9498557-9dd8-4086-bfe6-440cc515398a"]
}, Closed]],

Cell[CellGroupData[{

Cell["Matrices of reflections", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
  3.760629982671979*^9, 3.760629990092085*^9}, {3.760630171933566*^9, 
  3.760630181461022*^9}, {3.760632417848068*^9, 
  3.760632422351159*^9}},ExpressionUUID->"7e737d73-cc39-4cf9-af68-\
57d9476e8d7c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s1", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.7606323547650347`*^9, 3.760632356271002*^9}},
 CellLabel->
  "In[147]:=",ExpressionUUID->"dc8b00c0-699f-4106-950d-9f8e7a350a6d"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760632362261162*^9, 3.762428543581601*^9, 
  3.762428951282324*^9, 3.7624290536061287`*^9, 3.7624292453107777`*^9, 
  3.7624297331612997`*^9, 3.7624298086711807`*^9, 3.7629382469441442`*^9, 
  3.782221637569232*^9, 3.7822217595047073`*^9, 3.7822231171881447`*^9, 
  3.782223152491398*^9, 3.782547512394314*^9, 3.7825526323937798`*^9, 
  3.782555517463382*^9},
 CellLabel->
  "Out[147]//MatrixForm=",ExpressionUUID->"6fdfa763-664d-44e9-ac4a-\
9ffde231a70f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s2", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.760632385278757*^9, 3.7606323853989058`*^9}},
 CellLabel->
  "In[148]:=",ExpressionUUID->"e288c437-0db0-4f4d-8135-8f0f6e13934d"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0"},
     {"0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7606323864548187`*^9, 3.7624285464186697`*^9, 
  3.762428951348081*^9, 3.762429053671422*^9, 3.762429245377797*^9, 
  3.76242973322726*^9, 3.762429808736972*^9, 3.76293824699261*^9, 
  3.7822216375951777`*^9, 3.782221759536611*^9, 3.782223117225794*^9, 
  3.782223152534315*^9, 3.782547512423753*^9, 3.78255263240843*^9, 
  3.782555517494371*^9},
 CellLabel->
  "Out[148]//MatrixForm=",ExpressionUUID->"ad6d44a8-f0b6-4861-ae06-\
a10f8f68ff36"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s3", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.7606323936124573`*^9, 3.7606323936793947`*^9}},
 CellLabel->
  "In[149]:=",ExpressionUUID->"a82dd587-5344-4842-999d-4ac4e4db0c93"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760632394725415*^9, 3.762428548900743*^9, 
  3.76242895141457*^9, 3.7624290537392178`*^9, 3.762429245443386*^9, 
  3.76242973329243*^9, 3.762429808803762*^9, 3.762938247062407*^9, 
  3.782221637602683*^9, 3.7822217595461473`*^9, 3.782223117233674*^9, 
  3.7822231525413437`*^9, 3.7825475124340067`*^9, 3.7825526324543543`*^9, 
  3.78255551750323*^9},
 CellLabel->
  "Out[149]//MatrixForm=",ExpressionUUID->"cea439b3-c540-4ee9-a259-\
3f4da5a213db"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s4", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.760632449784658*^9, 3.760632449860031*^9}},
 CellLabel->
  "In[150]:=",ExpressionUUID->"de143f0a-2f4f-4f38-a08f-88362606a4ab"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "1"},
     {"0", "0", "0", "0", "1", "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7606324511054173`*^9, 3.7624285513554153`*^9, 
  3.762428951481024*^9, 3.762429053804844*^9, 3.762429245510454*^9, 
  3.7624297333418627`*^9, 3.762429808870586*^9, 3.762938247128035*^9, 
  3.78222163763522*^9, 3.7822217595751343`*^9, 3.782223117273675*^9, 
  3.7822231525859528`*^9, 3.7825475124659433`*^9, 3.782552632477406*^9, 
  3.7825555175354147`*^9},
 CellLabel->
  "Out[150]//MatrixForm=",ExpressionUUID->"94865d70-6e80-4bc2-b172-\
fd9f456fa258"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s5", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.76063245590226*^9, 3.7606324559798326`*^9}},
 CellLabel->
  "In[151]:=",ExpressionUUID->"894f7f7f-a038-45c8-93ff-e8378c9c660d"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", 
      RowBox[{"-", "1"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7606324568987303`*^9, 3.762428553770928*^9, 
  3.762428951547762*^9, 3.762429053872171*^9, 3.76242924557793*^9, 
  3.762429733410685*^9, 3.762429808937051*^9, 3.762938247195013*^9, 
  3.7822216376451674`*^9, 3.7822217595828867`*^9, 3.782223117281358*^9, 
  3.782223152593072*^9, 3.782547512475082*^9, 3.7825526325243196`*^9, 
  3.782555517547227*^9},
 CellLabel->
  "Out[151]//MatrixForm=",ExpressionUUID->"2c9eae3f-f51a-4e4a-93d1-\
07d629e4ec68"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s6", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.7606324612676764`*^9, 3.760632461327094*^9}},
 CellLabel->
  "In[152]:=",ExpressionUUID->"e4d434a9-0646-41c7-85fd-a57f607b9ddf"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"3", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0", "0", "0"},
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"5", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760632462283785*^9, 3.762428555638295*^9, 
  3.762428951614793*^9, 3.762429053938693*^9, 3.762429245644042*^9, 
  3.762429733475613*^9, 3.762429809002898*^9, 3.7629382472610607`*^9, 
  3.78222163767163*^9, 3.782221759616261*^9, 3.7822231173205748`*^9, 
  3.782223152637944*^9, 3.782547512505842*^9, 3.78255263262152*^9, 
  3.7825555175756063`*^9},
 CellLabel->
  "Out[152]//MatrixForm=",ExpressionUUID->"fec1722f-342c-47e1-aa84-\
173978f264b6"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s7", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.760632467574613*^9, 3.760632467620661*^9}},
 CellLabel->
  "In[153]:=",ExpressionUUID->"b59c48cc-65c8-4a2a-9734-b456dadbb63d"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"7", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"5", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"5", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"5", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {"0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7606324687547407`*^9, 3.7624285588596373`*^9, 
  3.7624289516797047`*^9, 3.7624290540060453`*^9, 3.762429245710308*^9, 
  3.762429733543241*^9, 3.7624298090686083`*^9, 3.762938247345142*^9, 
  3.782221637684623*^9, 3.7822217596268873`*^9, 3.782223117330751*^9, 
  3.782223152647068*^9, 3.782547512515647*^9, 3.7825526326437273`*^9, 
  3.7825555175847187`*^9},
 CellLabel->
  "Out[153]//MatrixForm=",ExpressionUUID->"987b14b4-6a20-473e-97e8-\
a8711be656bc"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s8", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.760632473868348*^9, 3.76063247392799*^9}},
 CellLabel->
  "In[154]:=",ExpressionUUID->"aa029788-bbc4-4a54-be0e-bbca1b07515f"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"17", "+", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "5"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"5", "+", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"5", "+", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"5", "+", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"5", "+", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760632474640966*^9, 3.7624285606408052`*^9, 
  3.762428951746993*^9, 3.762429054072274*^9, 3.7624292457779284`*^9, 
  3.762429733609838*^9, 3.762429809137261*^9, 3.762938247423891*^9, 
  3.782221637711297*^9, 3.782221759657131*^9, 3.782223117365355*^9, 
  3.782223152690468*^9, 3.782547512545973*^9, 3.782552632694749*^9, 
  3.782555517616487*^9},
 CellLabel->
  "Out[154]//MatrixForm=",ExpressionUUID->"876ef01c-3f61-4fdb-9e51-\
e2e0680a85f3"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MatrixForm", "[", "s9", "]"}], " "}]], "Input",
 CellChangeTimes->{{3.7606324790005007`*^9, 3.760632479304027*^9}},
 CellLabel->
  "In[155]:=",ExpressionUUID->"42a329ed-796a-494e-94d3-2459a6c58abc"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"263", "+", 
         RowBox[{"117", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"29", "+", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"29", "+", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"29", "+", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"29", "+", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"7", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{
       FractionBox["3", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"65", "+", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "63"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{
       FractionBox["3", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"65", "+", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "63"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{
       FractionBox["3", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"65", "+", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "63"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{
       FractionBox["3", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"65", "+", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "63"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{
       FractionBox["3", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760632480462782*^9, 3.7624285632422256`*^9, 
  3.7624289518138227`*^9, 3.7624290541387653`*^9, 3.762429245843726*^9, 
  3.762429733677384*^9, 3.762429809204171*^9, 3.762938247550055*^9, 
  3.782221637721767*^9, 3.782221759665599*^9, 3.782223117376075*^9, 
  3.782223152701535*^9, 3.7825475125581217`*^9, 3.782552632721086*^9, 
  3.782555517627331*^9},
 CellLabel->
  "Out[155]//MatrixForm=",ExpressionUUID->"a687b228-bf5a-4327-9b83-\
e71b69e1a16e"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
An infinite-order orientation-reversing element \\delta in the kernel of \
retraction R\
\>", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
  3.760629982671979*^9, 3.760629990092085*^9}, {3.7606302283738327`*^9, 
  3.760630247815802*^9}, {3.762431157743984*^9, 
  3.762431158500445*^9}},ExpressionUUID->"aab84984-52da-463b-a117-\
0f46e675ce0c"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"delta5", "=", 
    RowBox[{"Simplify", "[", 
     RowBox[{"s1", ".", "s2", ".", "s3", ".", "s4", ".", "s7"}], "]"}]}], 
   ";"}], " "}], "\[IndentingNewLine]", 
 RowBox[{"MatrixForm", "[", "delta5", "]"}]}], "Input",
 CellChangeTimes->{{3.758415296056778*^9, 3.7584153081303625`*^9}, {
  3.7584824392905817`*^9, 3.758482458591383*^9}, {3.758482617271708*^9, 
  3.758482619601139*^9}, {3.7606302001741953`*^9, 3.7606302046235657`*^9}, {
  3.760630284934063*^9, 3.760630289932104*^9}, {3.760630369355485*^9, 
  3.7606303781375217`*^9}, {3.760632607432494*^9, 3.760632613130381*^9}, {
  3.780673865086239*^9, 3.780673881334611*^9}, {3.782221736509898*^9, 
  3.782221743395248*^9}, {3.7822230782661324`*^9, 3.782223083661153*^9}},
 CellLabel->
  "In[156]:=",ExpressionUUID->"348f548c-89dd-4901-95d4-d437baef595c"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"7", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {"0", "0", "0", "0", "0", "1"},
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"5", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"5", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{"5", "+", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {"0", "0", "0", "0", "1", "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{
  3.782221759767797*^9, {3.782223102675209*^9, 3.782223117412819*^9}, 
   3.78222315274627*^9, 3.782547512586212*^9, 3.782552632776043*^9, 
   3.782555517659238*^9},
 CellLabel->
  "Out[157]//MatrixForm=",ExpressionUUID->"26d30760-caa0-41be-8299-\
81572e14d3a3"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Eigenvalues", "[", "delta5", "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.782221770398148*^9, 3.782221776461481*^9}, {
  3.782223129035241*^9, 3.7822231304187813`*^9}},
 CellLabel->
  "In[158]:=",ExpressionUUID->"61ae4eec-2fcf-4039-ac02-54e3d562d8e6"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"2.471401168449618`", ",", 
   RowBox[{
    RowBox[{"-", "0.6289979718219574`"}], "+", 
    RowBox[{"0.7774069406969969`", " ", "\[ImaginaryI]"}]}], ",", 
   RowBox[{
    RowBox[{"-", "0.6289979718219574`"}], "-", 
    RowBox[{"0.7774069406969969`", " ", "\[ImaginaryI]"}]}], ",", 
   RowBox[{"-", "1.`"}], ",", "1.`", ",", "0.4046287639441917`"}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.782223117506577*^9, 3.7822231528013163`*^9}, 
   3.7825475126509333`*^9, 3.782552632850333*^9, 3.782555517690968*^9},
 CellLabel->
  "Out[158]=",ExpressionUUID->"1cb82485-3450-49c9-a842-de8afbb1c5e4"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"delta5", " ", "=", " ", 
   RowBox[{"Canonize", "[", "delta5", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"MatrixForm", "[", "delta5", "]"}]}], "Input",
 CellChangeTimes->{{3.7606328697463493`*^9, 3.760632870262163*^9}, {
   3.7606329238625393`*^9, 3.760632930788604*^9}, {3.7606333036926928`*^9, 
   3.760633315680459*^9}, {3.7606333653220167`*^9, 3.760633385803891*^9}, {
   3.760633532814952*^9, 3.760633544139464*^9}, {3.760633604034707*^9, 
   3.760633653730147*^9}, {3.76063369308379*^9, 3.760633763453644*^9}, 
   3.760633798096099*^9, {3.7606338520755796`*^9, 3.760633856548257*^9}, {
   3.760633936125524*^9, 3.760633949312004*^9}, {3.7624285983746233`*^9, 
   3.762428650353005*^9}},
 CellLabel->
  "In[159]:=",ExpressionUUID->"f491ef28-9662-4a36-8afc-b88e01b5663d"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"2", "+", 
       RowBox[{"3", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], "0", "0"},
     {"0", "0", "0", "0", "0", "1"},
     {
      RowBox[{"1", "+", 
       RowBox[{"3", " ", "W"}]}], 
      RowBox[{"-", "W"}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], "0", "0"},
     {
      RowBox[{"1", "+", 
       RowBox[{"3", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], 
      RowBox[{"-", "W"}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], "0", "0"},
     {
      RowBox[{"1", "+", 
       RowBox[{"3", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", "W"}], 
      RowBox[{"-", "W"}], "0", "0"},
     {"0", "0", "0", "0", "1", "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{
  3.760633949910128*^9, 3.760634008653639*^9, 3.762428573365055*^9, {
   3.762428621350041*^9, 3.76242865180964*^9}, 3.762428952272132*^9, 
   3.762429054539934*^9, 3.762429246379149*^9, 3.762429734160236*^9, 
   3.76242980968792*^9, 3.762938248178199*^9, 3.7822216377989283`*^9, 
   3.7822217601786747`*^9, 3.7822231178024063`*^9, 3.782223152999345*^9, 
   3.782547512853704*^9, 3.782552633070562*^9, 3.7825555178715754`*^9},
 CellLabel->
  "Out[160]//MatrixForm=",ExpressionUUID->"1e3ec0c3-6c7c-45a0-8d90-\
2781e31337a6"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Computing the orders of reductions of \\delta", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.7606302283738327`*^9, 
   3.760630247815802*^9}, {3.7606775728478603`*^9, 3.7606775752317867`*^9}, {
   3.760678057751779*^9, 3.7606780730029297`*^9}, {3.7624299543377132`*^9, 
   3.76242997076448*^9}, 
   3.762430104913699*^9},ExpressionUUID->"e8008585-aa71-4b4c-bc7f-\
394d3ac6bfe6"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"MatrixReductionOrder", "[", 
  RowBox[{"delta5", ",", "7"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"FactorInteger", "[", "%", "]"}]}], "Input",
 CellChangeTimes->{{3.762428578892212*^9, 3.762428588984833*^9}, {
  3.76242865388275*^9, 3.762428655438704*^9}, {3.762429207196787*^9, 
  3.762429221946576*^9}, {3.7624297456050663`*^9, 3.762429745778*^9}, {
  3.762429831551074*^9, 3.762429831751978*^9}, {3.762429919965001*^9, 
  3.762429920096058*^9}, {3.7822217951492577`*^9, 3.7822217953758373`*^9}, {
  3.782221948788598*^9, 3.782221949325441*^9}},
 CellLabel->
  "In[235]:=",ExpressionUUID->"afea84c4-2593-4643-be6d-fcfd748ce6d8"],

Cell[BoxData["800"], "Output",
 CellChangeTimes->{
  3.7624288250204763`*^9, {3.7624290345506277`*^9, 3.7624290546386843`*^9}, {
   3.762429214173872*^9, 3.762429246620535*^9}, {3.762429734542255*^9, 
   3.762429746790794*^9}, 3.762429810085197*^9, 3.762429844370185*^9, {
   3.762429907573041*^9, 3.762429937313488*^9}, 3.762938259463285*^9, 
   3.782221694016389*^9, 3.7822217602232323`*^9, 3.782221826650075*^9, 
   3.782221954321409*^9, 3.7822231185947123`*^9, 3.7822231537955503`*^9, 
   3.78254751360747*^9, 3.782552633955905*^9, 3.782555518650523*^9, 
   3.7825555727313232`*^9},
 CellLabel->
  "Out[235]=",ExpressionUUID->"90d67f5e-50b4-4601-b12c-f4fb124a8af6"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"2", ",", "5"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"5", ",", "2"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.7624288250204763`*^9, {3.7624290345506277`*^9, 3.7624290546386843`*^9}, {
   3.762429214173872*^9, 3.762429246620535*^9}, {3.762429734542255*^9, 
   3.762429746790794*^9}, 3.762429810085197*^9, 3.762429844370185*^9, {
   3.762429907573041*^9, 3.762429937313488*^9}, 3.762938259463285*^9, 
   3.782221694016389*^9, 3.7822217602232323`*^9, 3.782221826650075*^9, 
   3.782221954321409*^9, 3.7822231185947123`*^9, 3.7822231537955503`*^9, 
   3.78254751360747*^9, 3.782552633955905*^9, 3.782555518650523*^9, 
   3.782555572734214*^9},
 CellLabel->
  "Out[236]=",ExpressionUUID->"237e5bd2-aa22-4b2b-82cc-81e3d7e9fd5b"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"MatrixReductionOrder", "[", 
  RowBox[{"delta5", ",", "11"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"FactorInteger", "[", "%", "]"}]}], "Input",
 CellChangeTimes->{{3.762429990877653*^9, 3.762429990947919*^9}, {
  3.782221799311121*^9, 3.782221799522938*^9}, {3.782221836793622*^9, 
  3.782221848373493*^9}, {3.782221952110189*^9, 3.782221952416272*^9}},
 CellLabel->
  "In[237]:=",ExpressionUUID->"49f9084f-2002-4f2b-b28f-b68409b03219"],

Cell[BoxData["8052"], "Output",
 CellChangeTimes->{
  3.76242999822091*^9, 3.762938266468748*^9, 3.78222176047932*^9, {
   3.782221831071517*^9, 3.7822218496454077`*^9}, 3.782221956999105*^9, 
   3.782223126974495*^9, 3.782223162026491*^9, 3.782547521400754*^9, 
   3.782552644199551*^9, 3.78255552688868*^9, 3.78255558420325*^9},
 CellLabel->
  "Out[237]=",ExpressionUUID->"bc588c95-4216-4584-984d-9e4d533f0116"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"2", ",", "2"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"3", ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"11", ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"61", ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.76242999822091*^9, 3.762938266468748*^9, 3.78222176047932*^9, {
   3.782221831071517*^9, 3.7822218496454077`*^9}, 3.782221956999105*^9, 
   3.782223126974495*^9, 3.782223162026491*^9, 3.782547521400754*^9, 
   3.782552644199551*^9, 3.78255552688868*^9, 3.782555584206011*^9},
 CellLabel->
  "Out[238]=",ExpressionUUID->"668e7a88-1a0d-4d07-8f59-2e9e3714ef7c"]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Polytope P_6", "Section",
 CellChangeTimes->{{3.760634464119334*^9, 3.760634485916493*^9}, {
   3.760634734543194*^9, 3.76063473748796*^9}, 
   3.780673893573295*^9},ExpressionUUID->"47a8fc4c-6e8e-42bd-a89d-\
666e6aeddcaf"],

Cell[CellGroupData[{

Cell["Quadratic form associated to polytope P_6 in H^6", "Subsection",
 CellChangeTimes->{{3.760634464119334*^9, 3.760634485916493*^9}, {
  3.780673955829299*^9, 
  3.780673956607201*^9}},ExpressionUUID->"97266003-ed28-4f89-93bf-\
c9de57dcf5f0"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"q6", "[", 
    RowBox[{"{", 
     RowBox[{
     "x0_", ",", "x1_", ",", "x2_", ",", "x3_", ",", "x4_", ",", "x5_", ",", 
      "x6_"}], "}"}], "]"}], "=", 
   RowBox[{
    RowBox[{
     RowBox[{"-", "2"}], "w", " ", 
     SuperscriptBox["x0", "2"]}], "+", 
    SuperscriptBox["x1", "2"], "+", 
    SuperscriptBox["x2", "2"], "+", 
    SuperscriptBox["x3", "2"], "+", 
    SuperscriptBox["x4", "2"], "+", 
    SuperscriptBox["x5", "2"], "+", 
    SuperscriptBox["x6", "2"]}]}], ";"}]], "Input",
 CellChangeTimes->{{3.75833102477936*^9, 3.758331038483093*^9}, {
   3.758331108311313*^9, 3.758331114658369*^9}, {3.7583341660018034`*^9, 
   3.758334169783081*^9}, {3.7583346817301817`*^9, 3.7583346915199986`*^9}, {
   3.758334955891484*^9, 3.7583349570170317`*^9}, {3.7583351720451264`*^9, 
   3.758335174690775*^9}, {3.7583352241967697`*^9, 3.7583352249319587`*^9}, {
   3.7583358468129377`*^9, 3.7583358486468563`*^9}, {3.758482261701007*^9, 
   3.75848227158998*^9}, {3.758482635388925*^9, 3.758482642656907*^9}, {
   3.7606352777374372`*^9, 3.760635293527937*^9}, {3.760635674325315*^9, 
   3.760635675123458*^9}, {3.762878835305243*^9, 3.762878836195209*^9}, 
   3.780673947784831*^9},
 CellLabel->
  "In[165]:=",ExpressionUUID->"f0ba17d2-31c2-4128-bbe6-f3adc6aaa232"]
}, Closed]],

Cell[CellGroupData[{

Cell["Standard basis of R^{1,6}", "Subsection",
 CellChangeTimes->{{3.760634464119334*^9, 3.760634508034494*^9}, {
  3.760634743268852*^9, 
  3.760634744473783*^9}},ExpressionUUID->"e061deed-68c7-4187-9987-\
0d623e88884a"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{
    "v0", ",", "v1", ",", "v2", ",", "v3", ",", "v4", ",", "v5", ",", "v6"}], 
    "}"}], "=", 
   RowBox[{"IdentityMatrix", "[", "7", "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.741986259869416*^9, 3.7419862881029577`*^9}, {
  3.753271317323329*^9, 3.753271354773836*^9}, {3.754247538035009*^9, 
  3.7542475546382313`*^9}, {3.7542655074583955`*^9, 3.754265525374155*^9}, {
  3.7583347561999874`*^9, 3.7583347762341795`*^9}, {3.7584822744062696`*^9, 
  3.7584822957468653`*^9}, {3.7606352279477*^9, 3.760635249960392*^9}, {
  3.762938166036707*^9, 3.762938171277726*^9}},
 CellLabel->
  "In[166]:=",ExpressionUUID->"4ff6ad38-ff77-4843-bf05-8fd50564406a"]
}, Closed]],

Cell[CellGroupData[{

Cell["Reflection associated to a given root", "Subsection",
 CellChangeTimes->{{3.760634464119334*^9, 3.760634508034494*^9}, {
  3.760634743268852*^9, 
  3.7606347731325083`*^9}},ExpressionUUID->"aa03f94f-b333-4585-b848-\
2acaf610569f"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Ref", "[", 
    RowBox[{"{", 
     RowBox[{
     "x0_", ",", "x1_", ",", "x2_", ",", "x3_", ",", "x4_", ",", "x5_", ",", 
      "x6_"}], "}"}], "]"}], "=", 
   RowBox[{"Join", "[", 
    RowBox[{
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v0", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"-", "2"}], "w"}], " ", ")"}], "x0"}], 
          RowBox[{"q6", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
             "x6"}], "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
           "x6"}], "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v1", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x1"}], 
          RowBox[{"q6", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
             "x6"}], "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
           "x6"}], "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v2", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x2"}], 
          RowBox[{"q6", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
             "x6"}], "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
           "x6"}], "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v3", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x3"}], 
          RowBox[{"q6", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
             "x6"}], "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
           "x6"}], "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v4", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x4"}], 
          RowBox[{"q6", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
             "x6"}], "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
           "x6"}], "}"}]}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v5", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x5"}], 
          RowBox[{"q6", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
             "x6"}], "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
           "x6"}], "}"}]}]}], "}"}], "]"}], ",", 
     RowBox[{"Transpose", "[", 
      RowBox[{"{", 
       RowBox[{"v6", "-", 
        RowBox[{
         FractionBox[
          RowBox[{"2", "x6"}], 
          RowBox[{"q6", "[", 
           RowBox[{"{", 
            RowBox[{
            "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
             "x6"}], "}"}], "]"}]], 
         RowBox[{"{", 
          RowBox[{
          "x0", ",", "x1", ",", "x2", ",", "x3", ",", "x4", ",", "x5", ",", 
           "x6"}], "}"}]}]}], "}"}], "]"}], ",", "2"}], "]"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.7419861662679973`*^9, 3.7419861761840124`*^9}, {
   3.741986397973914*^9, 3.7419863984046836`*^9}, {3.7419865314867964`*^9, 
   3.7419866452488146`*^9}, {3.741986676801154*^9, 3.741986699662715*^9}, {
   3.741986809738979*^9, 3.7419868540035834`*^9}, {3.7419869831504*^9, 
   3.7419870170933113`*^9}, {3.741987080457083*^9, 3.741987088644579*^9}, {
   3.741987197372342*^9, 3.7419872045821376`*^9}, {3.7419876787092505`*^9, 
   3.7419877098634653`*^9}, {3.7532717074829807`*^9, 3.753271708252512*^9}, {
   3.7532717520134134`*^9, 3.753271759361166*^9}, {3.7532730370434628`*^9, 
   3.7532731721369133`*^9}, {3.7532734653537464`*^9, 3.753273465911433*^9}, {
   3.75424756342313*^9, 3.754247597963746*^9}, {3.754265530814376*^9, 
   3.7542655829707956`*^9}, {3.758334783812334*^9, 3.7583348374824924`*^9}, {
   3.7583349364540243`*^9, 3.7583349374508185`*^9}, {3.758335043798848*^9, 
   3.7583350976989965`*^9}, {3.758335357866407*^9, 3.7583353596585617`*^9}, {
   3.758482645188974*^9, 3.7584826689002147`*^9}, {3.7584827464773893`*^9, 
   3.7584828299418893`*^9}, {3.760635266600648*^9, 3.7606352675061283`*^9}, {
   3.760635335545765*^9, 3.7606353965913877`*^9}, {3.760635577210795*^9, 
   3.760635594543326*^9}, {3.762749323086028*^9, 3.7627493248780518`*^9}, 
   3.780675133521154*^9},
 CellLabel->
  "In[167]:=",ExpressionUUID->"bdf04f4e-8925-4d62-a13f-05cc2ab9c8f2"]
}, Closed]],

Cell[CellGroupData[{

Cell["Outer normals for P_6 determined by Vinberg\[CloseCurlyQuote]s \
algorithm", "Subsection",
 CellChangeTimes->{{3.760634464119334*^9, 3.760634508034494*^9}, {
   3.760634743268852*^9, 3.760634744473783*^9}, {3.76063480212357*^9, 
   3.76063481057156*^9}, {3.7606348709661922`*^9, 3.760634876894898*^9}, 
   3.760634908164542*^9, {3.7606350989457808`*^9, 
   3.7606350992455683`*^9}},ExpressionUUID->"40306132-7397-49b0-a9d5-\
fa65325f9781"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"e1", "=", 
   RowBox[{
    RowBox[{"-", "v1"}], "+", "v2"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e2", "=", 
   RowBox[{
    RowBox[{"-", "v2"}], "+", "v3"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e3", "=", 
   RowBox[{
    RowBox[{"-", "v3"}], "+", "v4"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e4", "=", 
   RowBox[{
    RowBox[{"-", "v4"}], "+", "v5"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e5", "=", 
   RowBox[{
    RowBox[{"-", "v5"}], "+", "v6"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e6", "=", 
   RowBox[{"-", "v6"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e7", "=", 
   RowBox[{"v0", "+", 
    RowBox[{"w", 
     RowBox[{"(", 
      RowBox[{"v1", "+", "v2"}], ")"}]}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e8", "=", 
   RowBox[{"w", 
    RowBox[{"(", 
     RowBox[{"v0", "+", "v1", "+", "v2", "+", "v3", "+", "v4"}], ")"}]}]}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{"e9", "=", 
   RowBox[{
    RowBox[{"w", " ", "v0"}], "+", 
    RowBox[{"2", "w", " ", "v1"}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e10", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", "w"}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v0", "+", "v1", "+", "v2"}], ")"}]}], "+", 
    RowBox[{"w", 
     RowBox[{"(", 
      RowBox[{"v3", "+", "v4", "+", "v5", "+", "v6"}], ")"}]}]}]}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{"e11", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"3", "w"}]}], ")"}], "v1"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", "w"}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v2", "+", "v3", "+", "v4"}], ")"}]}], "+", 
    RowBox[{"w", 
     RowBox[{"(", 
      RowBox[{"v5", "+", "v6"}], ")"}]}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e12", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"3", "w"}]}], ")"}], "v1"}], "+", 
    RowBox[{"w", 
     RowBox[{"(", 
      RowBox[{"v2", "+", "v3", "+", "v4", "+", "v5", "+", "v6"}], ")"}]}]}]}],
   ";"}], "\n", 
 RowBox[{
  RowBox[{"e13", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"2", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", "w"}]}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v1", "+", "v2", "+", "v3", "+", "v4", "+", "v5"}], ")"}]}], 
    "+", "v6"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e14", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"3", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"4", "w"}]}], ")"}], "v1"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"2", "w"}]}], ")"}], "v2"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", "w"}]}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v3", "+", "v4", "+", "v5"}], ")"}]}], "+", "v6"}]}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{"e15", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"3", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"3", "+", 
       RowBox[{"4", "w"}]}], ")"}], "v1"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", "w"}]}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v2", "+", "v3", "+", "v4"}], ")"}]}], "+", 
    RowBox[{"2", "w", " ", "v5"}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e16", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"4", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"3", "+", 
       RowBox[{"6", "w"}]}], ")"}], "v1"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"2", "w"}]}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v2", "+", "v3", "+", "v4", "+", "v5"}], ")"}]}], "+", "v6"}]}],
   ";"}], "\n", 
 RowBox[{
  RowBox[{"e17", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"3", "+", 
       RowBox[{"4", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"5", "w"}]}], ")"}], "v1"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"3", "w"}]}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v2", "+", "v3", "+", "v4", "+", "v5"}], ")"}]}], "+", 
    RowBox[{"w", " ", "v6"}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"e18", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"4", "+", 
       RowBox[{"5", "w"}]}], ")"}], "v0"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"4", "+", 
       RowBox[{"6", "w"}]}], ")"}], "v1"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"2", "+", 
       RowBox[{"4", "w"}]}], ")"}], 
     RowBox[{"(", 
      RowBox[{"v2", "+", "v3", "+", "v4", "+", "v5"}], ")"}]}]}]}], 
  ";"}]}], "Input",
 CellChangeTimes->{{3.754247605639076*^9, 3.7542476463376746`*^9}, {
   3.7542476909997272`*^9, 3.75424769576234*^9}, {3.754247748432776*^9, 
   3.754247752456495*^9}, {3.754265587640855*^9, 3.754265606522153*^9}, {
   3.7545023480007434`*^9, 3.7545023590527573`*^9}, {3.7545109786068277`*^9, 
   3.7545109812052712`*^9}, {3.754511856874744*^9, 3.7545118579452834`*^9}, {
   3.754514337201006*^9, 3.7545143449562993`*^9}, {3.7545143775505514`*^9, 
   3.7545143816351643`*^9}, {3.7545732333107433`*^9, 3.754573243125018*^9}, {
   3.754573332704219*^9, 3.7545733464197054`*^9}, {3.754573421214228*^9, 
   3.7545734308343873`*^9}, {3.758334864665842*^9, 3.7583348976457005`*^9}, {
   3.758338393275598*^9, 3.7583384079328585`*^9}, {3.758338488110174*^9, 
   3.758338491281543*^9}, {3.7583385591617184`*^9, 3.758338570176575*^9}, {
   3.7583388441845007`*^9, 3.7583388547033725`*^9}, {3.758338926475912*^9, 
   3.758338927223629*^9}, {3.7583389690481977`*^9, 3.7583389747994957`*^9}, {
   3.758339012087595*^9, 3.7583390124548397`*^9}, {3.758339085369973*^9, 
   3.758339087635461*^9}, {3.7583391562305837`*^9, 3.758339240737707*^9}, {
   3.7583400755654745`*^9, 3.758340093254896*^9}, {3.758413246971608*^9, 
   3.758413269266621*^9}, {3.758413318231089*^9, 3.758413321220416*^9}, {
   3.758413437096233*^9, 3.7584134502654295`*^9}, {3.7584828377920403`*^9, 
   3.758483016025817*^9}, {3.760634883555806*^9, 3.7606349023906403`*^9}, {
   3.7606354201611834`*^9, 3.7606354241555433`*^9}, {3.7606354555051928`*^9, 
   3.760635525109261*^9}, 3.760677151025236*^9, {3.7806741171094713`*^9, 
   3.780674312570333*^9}, {3.780674354325041*^9, 3.7806747219045773`*^9}, {
   3.78067476105464*^9, 3.78067476547115*^9}, 3.782221424911798*^9, {
   3.782547411776787*^9, 3.7825474210550547`*^9}},
 CellLabel->
  "In[168]:=",ExpressionUUID->"d13fe9a6-d139-43c3-a145-fbce445a00e6"]
}, Closed]],

Cell[CellGroupData[{

Cell["Reflections in the bounding hyperplanes of P_6", "Subsection",
 CellChangeTimes->{{3.760634464119334*^9, 3.760634508034494*^9}, {
  3.760634743268852*^9, 3.760634744473783*^9}, {3.760634926701776*^9, 
  3.760634932832596*^9}, {3.760635075103628*^9, 
  3.760635095693418*^9}},ExpressionUUID->"2054d7a2-2a6e-484d-a4d7-\
ac8bc7878588"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"s1", "=", 
   RowBox[{"Ref", "[", "e1", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s2", "=", 
   RowBox[{"Ref", "[", "e2", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s3", "=", 
   RowBox[{"Ref", "[", "e3", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s4", "=", 
   RowBox[{"Ref", "[", "e4", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s5", "=", 
   RowBox[{"Ref", "[", "e5", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s6", "=", 
   RowBox[{"Ref", "[", "e6", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s7", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e7", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s8", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e8", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s9", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e9", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s10", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e10", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s11", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e11", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s12", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e12", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s13", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e13", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s14", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e14", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s15", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e15", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s16", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e16", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s17", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e17", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"s18", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Ref", "[", "e18", "]"}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.7583349010431814`*^9, 3.7583349033210793`*^9}, {
   3.7583349411761537`*^9, 3.7583349412939816`*^9}, {3.758335374359543*^9, 
   3.758335432323221*^9}, {3.75834115524435*^9, 3.7583411844974585`*^9}, {
   3.758413279687951*^9, 3.7584132884369483`*^9}, {3.758413462371809*^9, 
   3.7584134717453995`*^9}, {3.7584830515937543`*^9, 3.7584830663188906`*^9}, 
   3.758550669474656*^9, {3.760635113072641*^9, 3.760635150575037*^9}, {
   3.76063555893176*^9, 3.760635559624592*^9}, {3.780674961311529*^9, 
   3.780675017112917*^9}},
 CellLabel->
  "In[186]:=",ExpressionUUID->"1c552a10-4f02-4099-9824-0083c0261e8d"]
}, Closed]],

Cell[CellGroupData[{

Cell["Matrices of reflections", "Subsection",
 CellChangeTimes->{{3.760634464119334*^9, 3.760634485916493*^9}, {
  3.760634734543194*^9, 3.76063473748796*^9}, {3.760636105468917*^9, 
  3.760636110073513*^9}},ExpressionUUID->"03dda60b-329d-4ee3-92e6-\
be2355fa9ab0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s1", "]"}]], "Input",
 CellChangeTimes->{{3.7606355651667013`*^9, 3.760635569520255*^9}},
 CellLabel->
  "In[204]:=",ExpressionUUID->"7a7de1d1-8557-4bb9-ac95-8e9485269911"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760635570458552*^9, 3.760635613285615*^9, 
  3.760635660184409*^9, 3.76063569115554*^9, 3.76242905495846*^9, 
  3.762429246760681*^9, 3.762429734843877*^9, 3.762429810203473*^9, 
  3.762938266813518*^9, 3.782221762187459*^9, 3.782223127174403*^9, 
  3.782223162206341*^9, 3.782547455831162*^9, 3.7825475229670143`*^9, 
  3.782552645924055*^9, 3.782555527009535*^9},
 CellLabel->
  "Out[204]//MatrixForm=",ExpressionUUID->"7a87aaf1-d9ba-4c0e-a602-\
cf56199bf170"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s2", "]"}]], "Input",
 CellChangeTimes->{{3.760635696720151*^9, 3.760635701671376*^9}},
 CellLabel->
  "In[205]:=",ExpressionUUID->"e8db11e8-d76c-4c71-b1ba-138d7940e710"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760635702552224*^9, 3.762429055025792*^9, 
  3.762429246811056*^9, 3.762429734892947*^9, 3.7624298102705917`*^9, 
  3.762938266871258*^9, 3.78222176223428*^9, 3.7822231272258177`*^9, 
  3.782223162256723*^9, 3.782547458587715*^9, 3.7825475230024242`*^9, 
  3.7825526459332457`*^9, 3.78255552705645*^9},
 CellLabel->
  "Out[205]//MatrixForm=",ExpressionUUID->"de927c34-fd85-444c-92a1-\
35b836780d51"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s3", "]"}]], "Input",
 CellChangeTimes->{{3.760635704534789*^9, 3.760635708824257*^9}},
 CellLabel->
  "In[206]:=",ExpressionUUID->"3b31b563-f2ee-4e4f-a2fd-a03a1efdb428"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760635709587878*^9, 3.762429055091337*^9, 
  3.762429246859625*^9, 3.762429734976973*^9, 3.762429810337112*^9, 
  3.762938266939075*^9, 3.782221762246331*^9, 3.7822231272347383`*^9, 
  3.782223162268353*^9, 3.782547523013447*^9, 3.782552645964486*^9, 
  3.78255552706639*^9},
 CellLabel->
  "Out[206]//MatrixForm=",ExpressionUUID->"5cb1e98f-0dba-494d-ab40-\
ee92a0b74f87"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s4", "]"}]], "Input",
 CellChangeTimes->{{3.7606360169388533`*^9, 3.760636023512166*^9}},
 CellLabel->
  "In[207]:=",ExpressionUUID->"4df2c94b-d369-4675-a555-dfb3697d407d"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7606360243533983`*^9, 3.762429055157823*^9, 
  3.7624292469609337`*^9, 3.76242973509262*^9, 3.762429810454739*^9, 
  3.762938267005227*^9, 3.7822217622869873`*^9, 3.7822231272895403`*^9, 
  3.782223162318254*^9, 3.7825475230485067`*^9, 3.782552645974481*^9, 
  3.782555527112071*^9},
 CellLabel->
  "Out[207]//MatrixForm=",ExpressionUUID->"9326272d-ca31-4d71-b1f8-\
de5101435bce"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s5", "]"}]], "Input",
 CellChangeTimes->{{3.760636026257296*^9, 3.7606360316710453`*^9}},
 CellLabel->
  "In[208]:=",ExpressionUUID->"88d7ddd9-f4bf-434c-b0f3-2dae434e8d03"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "0", "1"},
     {"0", "0", "0", "0", "0", "1", "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760636032559081*^9, 3.762429055225966*^9, 
  3.762429247127042*^9, 3.762429735243354*^9, 3.76242981062113*^9, 
  3.7629382670682583`*^9, 3.7822217622988586`*^9, 3.78222312730044*^9, 
  3.782223162327394*^9, 3.782547523065569*^9, 3.7825526460021753`*^9, 
  3.782555527122089*^9},
 CellLabel->
  "Out[208]//MatrixForm=",ExpressionUUID->"a4e369f0-37db-4c13-9ae8-\
4e4447f6b65d"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s6", "]"}]], "Input",
 CellChangeTimes->{{3.7606360345571117`*^9, 3.760636039453999*^9}},
 CellLabel->
  "In[209]:=",ExpressionUUID->"86ddfb75-f870-4c0e-b87b-04236037fd20"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0", "0", "0", "0"},
     {"0", "1", "0", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "0", 
      RowBox[{"-", "1"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760636040230762*^9, 3.762429055291964*^9, 
  3.762429247228101*^9, 3.76242973577687*^9, 3.762429810769369*^9, 
  3.762938267137912*^9, 3.7822217623396273`*^9, 3.782223127350635*^9, 
  3.782223162376409*^9, 3.782547523101718*^9, 3.782552646011188*^9, 
  3.782555527168023*^9},
 CellLabel->
  "Out[209]//MatrixForm=",ExpressionUUID->"862df36b-a537-4de7-9c62-\
7e0c0d49f4fb"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s7", "]"}]], "Input",
 CellChangeTimes->{{3.7606360427860603`*^9, 3.760636047280512*^9}},
 CellLabel->
  "In[210]:=",ExpressionUUID->"7f6428f9-2537-423d-8dcb-86763fdd7d27"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"2", "+", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0", "0", "0"},
     {
      RowBox[{"3", "+", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0", "0", "0"},
     {
      RowBox[{"3", "+", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7606360484229403`*^9, 3.7624290553584003`*^9, 
  3.762429247277516*^9, 3.762429735959394*^9, 3.762429810853393*^9, 
  3.762938267203821*^9, 3.7822217623517237`*^9, 3.782223127363402*^9, 
  3.782223162388526*^9, 3.782547523112574*^9, 3.7825526460395327`*^9, 
  3.782555527176218*^9},
 CellLabel->
  "Out[210]//MatrixForm=",ExpressionUUID->"8fae6d5c-2e41-4e49-89ff-\
0b8bd4b48ef5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s8", "]"}]], "Input",
 CellChangeTimes->{{3.760636050337884*^9, 3.760636055108347*^9}},
 CellLabel->
  "In[211]:=",ExpressionUUID->"aa6a9e34-296b-4ad9-8608-8ea7adb7ed9a"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"5", "+", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], "0", "0"},
     {"0", "0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7606360562751093`*^9, 3.76242905542599*^9, 
  3.762429247328104*^9, 3.762429736093732*^9, 3.76242981090274*^9, 
  3.7629382673206873`*^9, 3.7822217623929853`*^9, 3.782223127415942*^9, 
  3.782223162435774*^9, 3.782547523151619*^9, 3.7825526460504932`*^9, 
  3.782555527228825*^9},
 CellLabel->
  "Out[211]//MatrixForm=",ExpressionUUID->"e4cb5e86-6703-45cb-8e02-\
7f81b883bfb4"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s9", "]"}]], "Input",
 CellChangeTimes->{{3.760636058350872*^9, 3.7606360635656433`*^9}},
 CellLabel->
  "In[212]:=",ExpressionUUID->"e0f54638-75a1-449a-9841-76f7cb67e3ec"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"5", "+", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "3"}], "-", 
       SqrtBox["5"]}], "0", "0", "0", "0", "0"},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "5"}], "-", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], "0", "0", "0", "0", "0"},
     {"0", "0", "1", "0", "0", "0", "0"},
     {"0", "0", "0", "1", "0", "0", "0"},
     {"0", "0", "0", "0", "1", "0", "0"},
     {"0", "0", "0", "0", "0", "1", "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.760636064415887*^9, 3.762429055538604*^9, 
  3.762429247380917*^9, 3.762429736243114*^9, 3.762429810954846*^9, 
  3.7629382674800787`*^9, 3.782221762403739*^9, 3.782223127427718*^9, 
  3.782223162446519*^9, 3.782547523163145*^9, 3.7825526460780573`*^9, 
  3.782555527238805*^9},
 CellLabel->
  "Out[212]//MatrixForm=",ExpressionUUID->"2e731fc5-1609-4e0b-b1f6-\
8643f9f27d7a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s10", "]"}]], "Input",
 CellChangeTimes->{{3.780675043136072*^9, 3.780675043492216*^9}},
 CellLabel->
  "In[213]:=",ExpressionUUID->"12fbe844-c489-4b64-8575-1f665d7297c0"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"12", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "5"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "5"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"7", "+", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"7", "+", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"7", "+", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"7", "+", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.782221762447897*^9, 3.78222312748248*^9, 
  3.7822231624966993`*^9, 3.7825475232008533`*^9, 3.782552646089555*^9, 
  3.782555527285911*^9},
 CellLabel->
  "Out[213]//MatrixForm=",ExpressionUUID->"2d87cdc9-e0ce-4d51-873a-\
b04739110d14"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s11", "]"}]], "Input",
 CellChangeTimes->{{3.78067504824791*^9, 3.780675048520174*^9}},
 CellLabel->
  "In[214]:=",ExpressionUUID->"8b813d86-442c-4591-85d8-9a09b379c4bf"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"30", "+", 
       RowBox[{"13", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "25"}], "-", 
         RowBox[{"11", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"40", "+", 
       RowBox[{"18", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"11", "+", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "5"}], "-", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "5"}], "-", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}]},
     {
      RowBox[{"18", "+", 
       RowBox[{"8", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "5"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"18", "+", 
       RowBox[{"8", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "5"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"18", "+", 
       RowBox[{"8", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "5"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "5"}], "-", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "5"}], "-", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.782221762461657*^9, 3.782223127495742*^9, 
  3.782223162510494*^9, 3.782547523214272*^9, 3.782552646120907*^9, 
  3.782555527295418*^9},
 CellLabel->
  "Out[214]//MatrixForm=",ExpressionUUID->"afaecca2-8d0a-4b77-a15e-\
135faec92ada"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s12", "]"}]], "Input",
 CellChangeTimes->{{3.780675052071847*^9, 3.780675052215498*^9}},
 CellLabel->
  "In[215]:=",ExpressionUUID->"cc593f67-7c38-4503-9d2b-686d309c0ec9"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"30", "+", 
       RowBox[{"13", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "29"}], "-", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"47", "+", 
       RowBox[{"21", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "3"}], "-", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7822217625056667`*^9, 3.782223127549267*^9, 
  3.782223162560689*^9, 3.782547523252201*^9, 3.7825526461330547`*^9, 
  3.7825555273448267`*^9},
 CellLabel->
  "Out[215]//MatrixForm=",ExpressionUUID->"2dae6e61-238f-4056-ad67-\
45423292f3f0"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s13", "]"}]], "Input",
 CellChangeTimes->{{3.780675056384*^9, 3.780675056560536*^9}},
 CellLabel->
  "In[216]:=",ExpressionUUID->"f17e7103-1581-4aaf-bd1a-e01267da1173"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"5", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "3"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.782221762519487*^9, 3.782223127563843*^9, 
  3.782223162575429*^9, 3.782547523266266*^9, 3.782552646163147*^9, 
  3.782555527356061*^9},
 CellLabel->
  "Out[216]//MatrixForm=",ExpressionUUID->"545d3f5c-897e-4b1d-9bae-\
e726170cf7d9"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s14", "]"}]], "Input",
 CellChangeTimes->{{3.780675060481843*^9, 3.780675060826679*^9}},
 CellLabel->
  "In[217]:=",ExpressionUUID->"2cab1fe6-d0ab-46ad-8359-2ca694428425"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"77", "+", 
       RowBox[{"34", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "29"}], "-", 
       RowBox[{"13", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "29"}], "-", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "29"}], "-", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "29"}], "-", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "7"}], "-", 
         RowBox[{"3", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"94", "+", 
       RowBox[{"42", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "35"}], "-", 
       RowBox[{"16", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"11", "+", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"58", "+", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"11", "+", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "13"}], "-", 
       RowBox[{"6", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "3"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"47", "+", 
       RowBox[{"21", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"47", "+", 
       RowBox[{"21", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"47", "+", 
       RowBox[{"21", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"11", "+", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "3"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.782221762561735*^9, 3.782223127616829*^9, 
  3.782223162623568*^9, 3.7825475233120337`*^9, 3.782552646174282*^9, 
  3.782555527405099*^9},
 CellLabel->
  "Out[217]//MatrixForm=",ExpressionUUID->"42757452-d4a4-40fb-adf8-\
7e0907df8c69"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s15", "]"}]], "Input",
 CellChangeTimes->{{3.78067506401091*^9, 3.780675064459339*^9}},
 CellLabel->
  "In[218]:=",ExpressionUUID->"0fe01854-b506-4936-a55c-53b2b51d4c8f"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"77", "+", 
       RowBox[{"34", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "29"}], "-", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "29"}], "-", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "29"}], "-", 
         RowBox[{"13", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "11"}], "-", 
       RowBox[{"5", " ", 
        SqrtBox["5"]}]}], "0"},
     {
      RowBox[{"105", "+", 
       RowBox[{"47", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"11", "+", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "20"}], "-", 
       RowBox[{"9", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "20"}], "-", 
       RowBox[{"9", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "20"}], "-", 
       RowBox[{"9", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "15"}], "-", 
       RowBox[{"7", " ", 
        SqrtBox["5"]}]}], "0"},
     {
      RowBox[{"47", "+", 
       RowBox[{"21", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "20"}], "-", 
       RowBox[{"9", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "7"}], "-", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], "0"},
     {
      RowBox[{"47", "+", 
       RowBox[{"21", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "20"}], "-", 
       RowBox[{"9", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "7"}], "-", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], "0"},
     {
      RowBox[{"47", "+", 
       RowBox[{"21", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "20"}], "-", 
       RowBox[{"9", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "7"}], "-", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], "0"},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "15"}], "-", 
       RowBox[{"7", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "7"}], "-", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "7"}], "-", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "7"}], "-", 
       RowBox[{"3", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "5"}], "-", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}], "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.782221762573206*^9, 3.782223127632964*^9, 
  3.7822231626376677`*^9, 3.7825475233258677`*^9, 3.782552646203383*^9, 
  3.78255552741465*^9},
 CellLabel->
  "Out[218]//MatrixForm=",ExpressionUUID->"7d09ec4f-ea27-46aa-8dd3-\
c324dc0b8ae2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s16", "]"}]], "Input",
 CellChangeTimes->{{3.780675067932077*^9, 3.780675068434495*^9}},
 CellLabel->
  "In[219]:=",ExpressionUUID->"60ec46e5-58cf-4517-8cb1-fe5ef63fb2b0"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"13", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "6"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"174", "+", 
       RowBox[{"78", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"20", "+", 
         RowBox[{"9", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"58", "+", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"58", "+", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"58", "+", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"58", "+", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"4", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"14", "+", 
       RowBox[{"6", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "3"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}], "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.782221762617476*^9, 3.782223127685102*^9, 
  3.7822231626863527`*^9, 3.782547523363381*^9, 3.7825526462148123`*^9, 
  3.782555527464836*^9},
 CellLabel->
  "Out[219]//MatrixForm=",ExpressionUUID->"fd8c1e92-c463-48c7-a597-\
3374896a8c5e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s17", "]"}]], "Input",
 CellChangeTimes->{{3.780675071632568*^9, 3.780675072310326*^9}},
 CellLabel->
  "In[220]:=",ExpressionUUID->"b3df6f7a-92ad-4567-84b7-118ec92a22d5"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"146", "+", 
       RowBox[{"65", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "95"}], "-", 
         RowBox[{"43", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "65"}], "-", 
         RowBox[{"29", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "15"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"155", "+", 
       RowBox[{"69", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "101"}], "-", 
         RowBox[{"45", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "69"}], "-", 
         RowBox[{"31", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "69"}], "-", 
         RowBox[{"31", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "69"}], "-", 
         RowBox[{"31", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "69"}], "-", 
         RowBox[{"31", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "17"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"105", "+", 
       RowBox[{"47", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "69"}], "-", 
         RowBox[{"31", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"105", "+", 
       RowBox[{"47", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "69"}], "-", 
         RowBox[{"31", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"105", "+", 
       RowBox[{"47", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "69"}], "-", 
         RowBox[{"31", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"105", "+", 
       RowBox[{"47", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "69"}], "-", 
         RowBox[{"31", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "47"}], "-", 
         RowBox[{"21", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}]},
     {
      RowBox[{"25", "+", 
       RowBox[{"11", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "17"}], "-", 
         RowBox[{"7", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "11"}], "-", 
         RowBox[{"5", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "-", 
         SqrtBox["5"]}], ")"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.782221762632183*^9, 3.7822231277001467`*^9, 
  3.782223162698337*^9, 3.782547523376997*^9, 3.782552646247052*^9, 
  3.7825555274748497`*^9},
 CellLabel->
  "Out[220]//MatrixForm=",ExpressionUUID->"298d89ae-b74f-4e60-8afc-\
e9618ab28404"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "[", "s18", "]"}]], "Input",
 CellChangeTimes->{{3.780675075629622*^9, 3.7806750764383507`*^9}},
 CellLabel->
  "In[221]:=",ExpressionUUID->"83bd893f-c7a1-4c62-8c6d-7ece882728f7"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"237", "+", 
       RowBox[{"106", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "83"}], "-", 
       RowBox[{"37", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "51"}], "-", 
       RowBox[{"23", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "51"}], "-", 
       RowBox[{"23", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "51"}], "-", 
       RowBox[{"23", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "51"}], "-", 
       RowBox[{"23", " ", 
        SqrtBox["5"]}]}], "0"},
     {
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"67", "+", 
         RowBox[{"30", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "93"}], "-", 
       RowBox[{"42", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "58"}], "-", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "58"}], "-", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "58"}], "-", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "58"}], "-", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], "0"},
     {
      RowBox[{"166", "+", 
       RowBox[{"74", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "58"}], "-", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "35"}], "-", 
       RowBox[{"16", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], "0"},
     {
      RowBox[{"166", "+", 
       RowBox[{"74", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "58"}], "-", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "35"}], "-", 
       RowBox[{"16", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], "0"},
     {
      RowBox[{"166", "+", 
       RowBox[{"74", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "58"}], "-", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "35"}], "-", 
       RowBox[{"16", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], "0"},
     {
      RowBox[{"166", "+", 
       RowBox[{"74", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "58"}], "-", 
       RowBox[{"26", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "4"}], " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "35"}], "-", 
       RowBox[{"16", " ", 
        SqrtBox["5"]}]}], "0"},
     {"0", "0", "0", "0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.782221762675445*^9, 3.7822231277532187`*^9, 
  3.782223162749895*^9, 3.7825475234214067`*^9, 3.782552646257906*^9, 
  3.782555527524785*^9},
 CellLabel->
  "Out[221]//MatrixForm=",ExpressionUUID->"299f6d33-f7e9-4932-be1c-\
8645536f9635"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
An infinite-order orientation-reversing element \\delta in the kernel of \
retraction R\
\>", "Subsection",
 CellChangeTimes->{{3.760634464119334*^9, 3.760634485916493*^9}, {
  3.760634734543194*^9, 3.76063473748796*^9}, {3.760636132276795*^9, 
  3.7606361468661547`*^9}, {3.762431129552492*^9, 
  3.762431129780154*^9}},ExpressionUUID->"6b9af708-aca5-4ed2-9649-\
67f8f4ad392a"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"delta6", "=", 
    RowBox[{"Simplify", "[", 
     RowBox[{"s7", ".", "s13", ".", "s18"}], "]"}]}], ";"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{"MatrixForm", "[", "delta6", "]"}]}], "Input",
 CellChangeTimes->{{3.758415296056778*^9, 3.7584153081303625`*^9}, {
  3.7584824392905817`*^9, 3.758482458591383*^9}, {3.758482617271708*^9, 
  3.758482619601139*^9}, {3.7584831141625404`*^9, 3.7584831281660757`*^9}, {
  3.7606360697054377`*^9, 3.760636081803093*^9}, {3.7606361534771547`*^9, 
  3.760636184027502*^9}, {3.780675082921237*^9, 3.7806750892101107`*^9}, {
  3.782222667155221*^9, 3.782222674975062*^9}, {3.7822236614065247`*^9, 
  3.782223665331593*^9}},
 CellLabel->
  "In[222]:=",ExpressionUUID->"e81fec8d-ea79-4cd7-b698-0ad442fbf35d"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"910", "+", 
       RowBox[{"407", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "623"}], "-", 
         RowBox[{"279", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "399"}], "-", 
         RowBox[{"179", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "199"}], "-", 
       RowBox[{"89", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "199"}], "-", 
       RowBox[{"89", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "199"}], "-", 
       RowBox[{"89", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"2", "+", 
         SqrtBox["5"]}], ")"}]}]},
     {
      RowBox[{"1053", "+", 
       RowBox[{"471", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "721"}], "-", 
         RowBox[{"323", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "463"}], "-", 
         RowBox[{"207", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "230"}], "-", 
       RowBox[{"103", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "230"}], "-", 
       RowBox[{"103", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "230"}], "-", 
       RowBox[{"103", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "5"}], "-", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}]},
     {
      RowBox[{"951", "+", 
       RowBox[{"425", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", 
        FractionBox["3", "2"]}], " ", 
       RowBox[{"(", 
        RowBox[{"217", "+", 
         RowBox[{"97", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "417"}], "-", 
         RowBox[{"187", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "208"}], "-", 
       RowBox[{"93", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "208"}], "-", 
       RowBox[{"93", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "208"}], "-", 
       RowBox[{"93", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "5"}], "-", 
       RowBox[{"2", " ", 
        SqrtBox["5"]}]}]},
     {
      RowBox[{"470", "+", 
       RowBox[{"210", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "161"}], "-", 
       RowBox[{"72", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"51", "+", 
         RowBox[{"23", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"470", "+", 
       RowBox[{"210", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "161"}], "-", 
       RowBox[{"72", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"51", "+", 
         RowBox[{"23", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"470", "+", 
       RowBox[{"210", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "161"}], "-", 
       RowBox[{"72", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "103"}], "-", 
       RowBox[{"46", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "2"}], " ", 
       RowBox[{"(", 
        RowBox[{"51", "+", 
         RowBox[{"23", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       SqrtBox["5"]}]},
     {
      RowBox[{"8", " ", 
       RowBox[{"(", 
        RowBox[{"9", "+", 
         RowBox[{"4", " ", 
          SqrtBox["5"]}]}], ")"}]}], 
      RowBox[{
       RowBox[{"-", "24"}], "-", 
       RowBox[{"11", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "16"}], "-", 
       RowBox[{"7", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "16"}], "-", 
       RowBox[{"7", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "16"}], "-", 
       RowBox[{"7", " ", 
        SqrtBox["5"]}]}], 
      RowBox[{
       RowBox[{"-", "16"}], "-", 
       RowBox[{"7", " ", 
        SqrtBox["5"]}]}], "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7584763329422874`*^9, 3.7584771619178305`*^9, 
  3.7584799303704815`*^9, 3.7584831395069013`*^9, 3.7585507431547613`*^9, 
  3.7585508711514273`*^9, 3.760636225475247*^9, 3.76242905565803*^9, 
  3.762429247465543*^9, 3.762429736326721*^9, 3.762429811002907*^9, 
  3.762938267553648*^9, 3.782221762685915*^9, 3.782223127864697*^9, 
  3.782223162761541*^9, 3.7822236687507877`*^9, 3.782547473487479*^9, 
  3.78254752403412*^9, 3.782547647769609*^9, 3.782552646937038*^9, 
  3.782555527536825*^9},
 CellLabel->
  "Out[223]//MatrixForm=",ExpressionUUID->"b858e4de-2f6d-425f-a3c5-\
0069af32ade4"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Eigenvalues", "[", "delta6", "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.782223676610248*^9, 3.782223683989717*^9}},
 CellLabel->
  "In[224]:=",ExpressionUUID->"79f97ed2-67d2-4bf8-aef2-f0352c6677e3"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"63.289151188684215`", ",", 
   RowBox[{"-", "1.`"}], ",", "1.`", ",", "1.`", ",", "1.`", ",", "1.`", ",", 
   "0.015800496312846662`"}], "}"}]], "Output",
 CellChangeTimes->{3.782223685538845*^9, 3.7825475241466913`*^9, 
  3.7825476515071707`*^9, 3.782552647049056*^9, 3.782555527614378*^9},
 CellLabel->
  "Out[224]=",ExpressionUUID->"13c88d6e-f2e3-40c6-8720-82bdc0959158"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"delta6", "=", 
   RowBox[{"Canonize", "[", "delta6", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"MatrixForm", "[", "delta6", "]"}]}], "Input",
 CellChangeTimes->{{3.7624300460940523`*^9, 3.7624300633744507`*^9}},
 CellLabel->
  "In[225]:=",ExpressionUUID->"0b25b621-273b-434a-9a8b-2e218eb44822"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"503", "+", 
       RowBox[{"814", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "172"}], "-", 
       RowBox[{"279", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "110"}], "-", 
       RowBox[{"179", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "110"}], "-", 
       RowBox[{"178", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "110"}], "-", 
       RowBox[{"178", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "110"}], "-", 
       RowBox[{"178", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "2"}], "-", 
       RowBox[{"4", " ", "W"}]}]},
     {
      RowBox[{"582", "+", 
       RowBox[{"942", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "199"}], "-", 
       RowBox[{"323", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "128"}], "-", 
       RowBox[{"207", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "127"}], "-", 
       RowBox[{"206", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "127"}], "-", 
       RowBox[{"206", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "127"}], "-", 
       RowBox[{"206", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "3"}], "-", 
       RowBox[{"4", " ", "W"}]}]},
     {
      RowBox[{"526", "+", 
       RowBox[{"850", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "180"}], "-", 
       RowBox[{"291", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "115"}], "-", 
       RowBox[{"187", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "115"}], "-", 
       RowBox[{"186", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "115"}], "-", 
       RowBox[{"186", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "115"}], "-", 
       RowBox[{"186", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "3"}], "-", 
       RowBox[{"4", " ", "W"}]}]},
     {
      RowBox[{"260", "+", 
       RowBox[{"420", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "89"}], "-", 
       RowBox[{"144", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "56"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", 
       RowBox[{"2", " ", "W"}]}]},
     {
      RowBox[{"260", "+", 
       RowBox[{"420", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "89"}], "-", 
       RowBox[{"144", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "56"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", 
       RowBox[{"2", " ", "W"}]}]},
     {
      RowBox[{"260", "+", 
       RowBox[{"420", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "89"}], "-", 
       RowBox[{"144", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "57"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "56"}], "-", 
       RowBox[{"92", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "1"}], "-", 
       RowBox[{"2", " ", "W"}]}]},
     {
      RowBox[{"40", "+", 
       RowBox[{"64", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "13"}], "-", 
       RowBox[{"22", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"14", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"14", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"14", " ", "W"}]}], 
      RowBox[{
       RowBox[{"-", "9"}], "-", 
       RowBox[{"14", " ", "W"}]}], "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.762430064940117*^9, 3.762938267647118*^9, 
  3.78222176272869*^9, 3.7822231284232607`*^9, 3.782223163333089*^9, 
  3.7822236923990088`*^9, 3.782547524685762*^9, 3.782547655297709*^9, 
  3.782552647608988*^9, 3.7825555281196003`*^9},
 CellLabel->
  "Out[226]//MatrixForm=",ExpressionUUID->"8fd7f63d-058d-4a51-b326-\
886b1106286b"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Computing the orders of reductions of \\delta", "Subsection",
 CellChangeTimes->{{3.7606298509619102`*^9, 3.760629902942297*^9}, {
   3.760629982671979*^9, 3.760629990092085*^9}, {3.7606302283738327`*^9, 
   3.760630247815802*^9}, {3.7606775728478603`*^9, 3.7606775752317867`*^9}, {
   3.760678057751779*^9, 3.7606780730029297`*^9}, {3.7624299543377132`*^9, 
   3.76242997076448*^9}, 
   3.762430098214566*^9},ExpressionUUID->"2c356fc7-7d65-4c10-8843-\
f074cd1d1693"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"MatrixReductionOrder", "[", 
  RowBox[{"delta6", ",", "7"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"FactorInteger", "[", "%", "]"}]}], "Input",
 CellChangeTimes->{{3.762428578892212*^9, 3.762428588984833*^9}, {
  3.76242865388275*^9, 3.762428655438704*^9}, {3.762429207196787*^9, 
  3.762429221946576*^9}, {3.7624297456050663`*^9, 3.762429745778*^9}, {
  3.762429831551074*^9, 3.762429831751978*^9}, {3.762429919965001*^9, 
  3.762429920096058*^9}, {3.762430070234456*^9, 3.762430070304302*^9}, {
  3.782555550080985*^9, 3.782555550263659*^9}},
 CellLabel->
  "In[231]:=",ExpressionUUID->"3cbda2eb-c6ef-4f25-bd5b-45be63516047"],

Cell[BoxData["8"], "Output",
 CellChangeTimes->{
  3.7624288250204763`*^9, {3.7624290345506277`*^9, 3.7624290546386843`*^9}, {
   3.762429214173872*^9, 3.762429246620535*^9}, {3.762429734542255*^9, 
   3.762429746790794*^9}, 3.762429810085197*^9, 3.762429844370185*^9, {
   3.762429907573041*^9, 3.762429937313488*^9}, 3.762430076576075*^9, 
   3.7629382731639843`*^9, 3.782221816641773*^9, 3.782223128736212*^9, 
   3.782223163648341*^9, 3.782223699690634*^9, 3.7825475247846518`*^9, 
   3.782552647718754*^9, {3.7825555282666187`*^9, 3.782555551695878*^9}},
 CellLabel->
  "Out[231]=",ExpressionUUID->"742e49e7-b82f-4a4a-8fe0-f18c468bdb90"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"2", ",", "3"}], "}"}], "}"}]], "Output",
 CellChangeTimes->{
  3.7624288250204763`*^9, {3.7624290345506277`*^9, 3.7624290546386843`*^9}, {
   3.762429214173872*^9, 3.762429246620535*^9}, {3.762429734542255*^9, 
   3.762429746790794*^9}, 3.762429810085197*^9, 3.762429844370185*^9, {
   3.762429907573041*^9, 3.762429937313488*^9}, 3.762430076576075*^9, 
   3.7629382731639843`*^9, 3.782221816641773*^9, 3.782223128736212*^9, 
   3.782223163648341*^9, 3.782223699690634*^9, 3.7825475247846518`*^9, 
   3.782552647718754*^9, {3.7825555282666187`*^9, 3.7825555516994963`*^9}},
 CellLabel->
  "Out[232]=",ExpressionUUID->"a0f15a31-e27f-481a-b166-1b4874c6f03f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"MatrixReductionOrder", "[", 
  RowBox[{"delta6", ",", "11"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"FactorInteger", "[", "%", "]"}]}], "Input",
 CellChangeTimes->{{3.762429990877653*^9, 3.762429990947919*^9}, {
  3.762430082469998*^9, 3.762430082513323*^9}, {3.782555555083748*^9, 
  3.782555555148419*^9}},
 CellLabel->
  "In[233]:=",ExpressionUUID->"1c60e7f5-a6f9-4d1e-87c3-ecaccf925aa5"],

Cell[BoxData["44"], "Output",
 CellChangeTimes->{
  3.76242999822091*^9, 3.76243008700937*^9, 3.762938276348153*^9, 
   3.782223128801672*^9, 3.782223163711872*^9, 3.78222370551648*^9, 
   3.7825475249034147`*^9, 3.782552647856626*^9, {3.7825555283943996`*^9, 
   3.7825555566133213`*^9}},
 CellLabel->
  "Out[233]=",ExpressionUUID->"e0be12ec-29b1-4714-b204-ed6aad44e0f6"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"2", ",", "2"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"11", ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.76242999822091*^9, 3.76243008700937*^9, 3.762938276348153*^9, 
   3.782223128801672*^9, 3.782223163711872*^9, 3.78222370551648*^9, 
   3.7825475249034147`*^9, 3.782552647856626*^9, {3.7825555283943996`*^9, 
   3.7825555566170397`*^9}},
 CellLabel->
  "Out[234]=",ExpressionUUID->"253c6d1e-cec1-449f-9ab1-ce6d9b556975"]
}, Open  ]]
}, Closed]]
}, Open  ]]
},
WindowSize->{1280, 637},
WindowMargins->{{Automatic, 0}, {61, Automatic}},
PrintingCopies->1,
PrintingPageRange->{32000, 32000},
PrintingOptions->{"Magnification"->1.,
"PaperOrientation"->"Portrait",
"PaperSize"->{612, 792}},
FrontEndVersion->"12.0 for Mac OS X x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[422, 15, 290, 5, 67, "Section",ExpressionUUID->"14656a38-3554-4a83-a92b-19dd9f26f677"],
Cell[CellGroupData[{
Cell[737, 24, 502, 7, 54, "Subsection",ExpressionUUID->"ba38d90f-9f56-4c32-ab1a-2c10dd50fb99"],
Cell[1242, 33, 299, 8, 47, "Input",ExpressionUUID->"523e1b05-8bc2-42dc-9699-1ee01a010fe5"]
}, Closed]],
Cell[CellGroupData[{
Cell[1578, 46, 494, 7, 38, "Subsection",ExpressionUUID->"e34f0406-b25e-4c04-be88-09fbbd2bc598"],
Cell[2075, 55, 225, 5, 30, "Input",ExpressionUUID->"9f07e933-6f88-438b-a93c-aa55e066714c"]
}, Closed]],
Cell[CellGroupData[{
Cell[2337, 65, 482, 8, 38, "Subsection",ExpressionUUID->"58d1b469-9b5a-4f36-a092-13feb4807ed2"],
Cell[2822, 75, 1261, 33, 52, "Input",ExpressionUUID->"0b6880d5-4523-48e5-b931-301e9c803020"]
}, Closed]],
Cell[CellGroupData[{
Cell[4120, 113, 522, 7, 38, "Subsection",ExpressionUUID->"9a31f9b5-514c-41e1-84a7-0ac90acebfa7"],
Cell[4645, 122, 736, 20, 52, "Input",ExpressionUUID->"bc731114-24c1-40b7-8ac2-67b8dedbc24a"]
}, Closed]],
Cell[CellGroupData[{
Cell[5418, 147, 564, 10, 38, "Subsection",ExpressionUUID->"8e02da97-769b-4a13-b665-f98fee9a0bdb"],
Cell[5985, 159, 1536, 40, 73, "Input",ExpressionUUID->"e3862526-5b9f-4a42-8dc3-dbdd97875f95"]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[7570, 205, 481, 7, 67, "Section",ExpressionUUID->"4fe39d2d-a7ae-47be-adfb-2dbc19ef7abc"],
Cell[CellGroupData[{
Cell[8076, 216, 422, 6, 54, "Subsection",ExpressionUUID->"586cf5a7-92da-4e89-8aad-2a8dbfa9eab8"],
Cell[8501, 224, 1382, 32, 30, "Input",ExpressionUUID->"6b64ac43-4543-44e4-b995-6564add16920"]
}, Closed]],
Cell[CellGroupData[{
Cell[9920, 261, 270, 4, 38, "Subsection",ExpressionUUID->"caa59798-9eb5-4c6f-84bf-6e76f6475984"],
Cell[10193, 267, 656, 13, 30, "Input",ExpressionUUID->"50a66ac0-62f9-4740-9d9d-ba0add622f50"]
}, Closed]],
Cell[CellGroupData[{
Cell[10886, 285, 286, 4, 38, "Subsection",ExpressionUUID->"0240d1ab-7609-44f6-84ae-bbc687460272"],
Cell[11175, 291, 3952, 117, 176, "Input",ExpressionUUID->"3d591a9f-e348-4576-b0b4-7bc2099d449c"]
}, Closed]],
Cell[CellGroupData[{
Cell[15164, 413, 319, 5, 38, "Subsection",ExpressionUUID->"242f1bf9-b52c-454f-a26c-f6c70bf4069e"],
Cell[15486, 420, 2303, 74, 199, "Input",ExpressionUUID->"1f1ee5de-24f9-47f0-a0e9-29be6458ba84"]
}, Closed]],
Cell[CellGroupData[{
Cell[17826, 499, 291, 4, 38, "Subsection",ExpressionUUID->"2ff5c21b-63ac-45d6-a0f5-f0dd525ead4b"],
Cell[18120, 505, 1608, 40, 199, "Input",ExpressionUUID->"c9498557-9dd8-4086-bfe6-440cc515398a"]
}, Closed]],
Cell[CellGroupData[{
Cell[19765, 550, 317, 5, 38, "Subsection",ExpressionUUID->"7e737d73-cc39-4cf9-af68-57d9476e8d7c"],
Cell[CellGroupData[{
Cell[20107, 559, 233, 5, 30, "Input",ExpressionUUID->"dc8b00c0-699f-4106-950d-9f8e7a350a6d"],
Cell[20343, 566, 1148, 28, 70, "Output",ExpressionUUID->"6fdfa763-664d-44e9-ac4a-9ffde231a70f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[21528, 599, 233, 5, 30, "Input",ExpressionUUID->"e288c437-0db0-4f4d-8135-8f0f6e13934d"],
Cell[21764, 606, 1135, 28, 70, "Output",ExpressionUUID->"ad6d44a8-f0b6-4861-ae06-a10f8f68ff36"]
}, Open  ]],
Cell[CellGroupData[{
Cell[22936, 639, 235, 5, 30, "Input",ExpressionUUID->"a82dd587-5344-4842-999d-4ac4e4db0c93"],
Cell[23174, 646, 1139, 28, 70, "Output",ExpressionUUID->"cea439b3-c540-4ee9-a259-3f4da5a213db"]
}, Open  ]],
Cell[CellGroupData[{
Cell[24350, 679, 231, 5, 30, "Input",ExpressionUUID->"de143f0a-2f4f-4f38-a08f-88362606a4ab"],
Cell[24584, 686, 1145, 28, 70, "Output",ExpressionUUID->"94865d70-6e80-4bc2-b172-fd9f456fa258"]
}, Open  ]],
Cell[CellGroupData[{
Cell[25766, 719, 232, 5, 30, "Input",ExpressionUUID->"894f7f7f-a038-45c8-93ff-e8378c9c660d"],
Cell[26001, 726, 1161, 29, 70, "Output",ExpressionUUID->"2c9eae3f-f51a-4e4a-93d1-07d629e4ec68"]
}, Open  ]],
Cell[CellGroupData[{
Cell[27199, 760, 233, 5, 30, "Input",ExpressionUUID->"e4d434a9-0646-41c7-85fd-a57f607b9ddf"],
Cell[27435, 767, 1702, 50, 70, "Output",ExpressionUUID->"fec1722f-342c-47e1-aa84-173978f264b6"]
}, Open  ]],
Cell[CellGroupData[{
Cell[29174, 822, 231, 5, 30, "Input",ExpressionUUID->"b59c48cc-65c8-4a2a-9734-b456dadbb63d"],
Cell[29408, 829, 3636, 124, 70, "Output",ExpressionUUID->"987b14b4-6a20-473e-97e8-a8711be656bc"]
}, Open  ]],
Cell[CellGroupData[{
Cell[33081, 958, 230, 5, 30, "Input",ExpressionUUID->"aa029788-bbc4-4a54-be0e-bbca1b07515f"],
Cell[33314, 965, 5388, 198, 70, "Output",ExpressionUUID->"876ef01c-3f61-4fdb-9e51-e2e0680a85f3"]
}, Open  ]],
Cell[CellGroupData[{
Cell[38739, 1168, 233, 5, 30, "Input",ExpressionUUID->"42a329ed-796a-494e-94d3-2459a6c58abc"],
Cell[38975, 1175, 7675, 273, 70, "Output",ExpressionUUID->"a687b228-bf5a-4327-9b83-e71b69e1a16e"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[46699, 1454, 391, 8, 38, "Subsection",ExpressionUUID->"aab84984-52da-463b-a117-0f46e675ce0c"],
Cell[CellGroupData[{
Cell[47115, 1466, 857, 16, 52, "Input",ExpressionUUID->"348f548c-89dd-4901-95d4-d437baef595c"],
Cell[47975, 1484, 3441, 122, 70, "Output",ExpressionUUID->"26d30760-caa0-41be-8299-81572e14d3a3"]
}, Open  ]],
Cell[CellGroupData[{
Cell[51453, 1611, 293, 6, 30, "Input",ExpressionUUID->"61ae4eec-2fcf-4039-ac02-54e3d562d8e6"],
Cell[51749, 1619, 631, 14, 70, "Output",ExpressionUUID->"1cb82485-3450-49c9-a842-de8afbb1c5e4"]
}, Open  ]],
Cell[CellGroupData[{
Cell[52417, 1638, 818, 14, 52, "Input",ExpressionUUID->"f491ef28-9662-4a36-8afc-b88e01b5663d"],
Cell[53238, 1654, 1950, 58, 70, "Output",ExpressionUUID->"1e3ec0c3-6c7c-45a0-8d90-2781e31337a6"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[55237, 1718, 473, 7, 38, "Subsection",ExpressionUUID->"e8008585-aa71-4b4c-bc7f-394d3ac6bfe6"],
Cell[CellGroupData[{
Cell[55735, 1729, 658, 11, 52, "Input",ExpressionUUID->"afea84c4-2593-4643-be6d-fcfd748ce6d8"],
Cell[56396, 1742, 669, 11, 68, "Output",ExpressionUUID->"90d67f5e-50b4-4601-b12c-f4fb124a8af6"],
Cell[57068, 1755, 808, 17, 34, "Output",ExpressionUUID->"237e5bd2-aa22-4b2b-82cc-81e3d7e9fd5b"]
}, Open  ]],
Cell[CellGroupData[{
Cell[57913, 1777, 464, 8, 52, "Input",ExpressionUUID->"49f9084f-2002-4f2b-b28f-b68409b03219"],
Cell[58380, 1787, 413, 7, 34, "Output",ExpressionUUID->"bc588c95-4216-4584-984d-9e4d533f0116"],
Cell[58796, 1796, 674, 17, 34, "Output",ExpressionUUID->"668e7a88-1a0d-4d07-8f59-2e9e3714ef7c"]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[59531, 1820, 229, 4, 67, "Section",ExpressionUUID->"47a8fc4c-6e8e-42bd-a89d-666e6aeddcaf"],
Cell[CellGroupData[{
Cell[59785, 1828, 245, 4, 54, "Subsection",ExpressionUUID->"97266003-ed28-4f89-93bf-c9de57dcf5f0"],
Cell[60033, 1834, 1317, 29, 30, "Input",ExpressionUUID->"f0ba17d2-31c2-4128-bbe6-f3adc6aaa232"]
}, Closed]],
Cell[CellGroupData[{
Cell[61387, 1868, 222, 4, 38, "Subsection",ExpressionUUID->"e061deed-68c7-4187-9987-0d623e88884a"],
Cell[61612, 1874, 723, 15, 30, "Input",ExpressionUUID->"4ff6ad38-ff77-4843-bf05-8fd50564406a"]
}, Closed]],
Cell[CellGroupData[{
Cell[62372, 1894, 236, 4, 38, "Subsection",ExpressionUUID->"aa03f94f-b333-4585-b848-2acaf610569f"],
Cell[62611, 1900, 5369, 138, 302, "Input",ExpressionUUID->"bdf04f4e-8925-4d62-a13f-05cc2ab9c8f2"]
}, Closed]],
Cell[CellGroupData[{
Cell[68017, 2043, 445, 7, 38, "Subsection",ExpressionUUID->"40306132-7397-49b0-a9d5-fa65325f9781"],
Cell[68465, 2052, 6956, 220, 388, "Input",ExpressionUUID->"d13fe9a6-d139-43c3-a145-fbce445a00e6"]
}, Closed]],
Cell[CellGroupData[{
Cell[75458, 2277, 338, 5, 38, "Subsection",ExpressionUUID->"2054d7a2-2a6e-484d-a4d7-ac8bc7878588"],
Cell[75799, 2284, 2910, 76, 388, "Input",ExpressionUUID->"1c552a10-4f02-4099-9824-0083c0261e8d"]
}, Closed]],
Cell[CellGroupData[{
Cell[78746, 2365, 265, 4, 38, "Subsection",ExpressionUUID->"03dda60b-329d-4ee3-92e6-be2355fa9ab0"],
Cell[CellGroupData[{
Cell[79036, 2373, 215, 4, 30, "Input",ExpressionUUID->"7a7de1d1-8557-4bb9-ac95-8e9485269911"],
Cell[79254, 2379, 1226, 29, 70, "Output",ExpressionUUID->"7a87aaf1-d9ba-4c0e-a602-cf56199bf170"]
}, Open  ]],
Cell[CellGroupData[{
Cell[80517, 2413, 213, 4, 30, "Input",ExpressionUUID->"e8db11e8-d76c-4c71-b1ba-138d7940e710"],
Cell[80733, 2419, 1163, 28, 70, "Output",ExpressionUUID->"de927c34-fd85-444c-92a1-35b836780d51"]
}, Open  ]],
Cell[CellGroupData[{
Cell[81933, 2452, 213, 4, 30, "Input",ExpressionUUID->"3b31b563-f2ee-4e4f-a2fd-a03a1efdb428"],
Cell[82149, 2458, 1136, 28, 70, "Output",ExpressionUUID->"5cb1e98f-0dba-494d-ab40-ee92a0b74f87"]
}, Open  ]],
Cell[CellGroupData[{
Cell[83322, 2491, 215, 4, 30, "Input",ExpressionUUID->"4df2c94b-d369-4675-a555-dfb3697d407d"],
Cell[83540, 2497, 1144, 28, 70, "Output",ExpressionUUID->"9326272d-ca31-4d71-b1f8-de5101435bce"]
}, Open  ]],
Cell[CellGroupData[{
Cell[84721, 2530, 215, 4, 30, "Input",ExpressionUUID->"88d7ddd9-f4bf-434c-b0f3-2dae434e8d03"],
Cell[84939, 2536, 1139, 28, 70, "Output",ExpressionUUID->"a4e369f0-37db-4c13-9ae8-4e4447f6b65d"]
}, Open  ]],
Cell[CellGroupData[{
Cell[86115, 2569, 215, 4, 30, "Input",ExpressionUUID->"86ddfb75-f870-4c0e-b87b-04236037fd20"],
Cell[86333, 2575, 1158, 29, 70, "Output",ExpressionUUID->"862df36b-a537-4de7-9c62-7e0c0d49f4fb"]
}, Open  ]],
Cell[CellGroupData[{
Cell[87528, 2609, 215, 4, 30, "Input",ExpressionUUID->"7f6428f9-2537-423d-8dcb-86763fdd7d27"],
Cell[87746, 2615, 2199, 70, 70, "Output",ExpressionUUID->"8fae6d5c-2e41-4e49-89ff-0b8bd4b48ef5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[89982, 2690, 213, 4, 30, "Input",ExpressionUUID->"aa6a9e34-296b-4ad9-8608-8ea7adb7ed9a"],
Cell[90198, 2696, 4706, 167, 70, "Output",ExpressionUUID->"e4cb5e86-6703-45cb-8e02-7f81b883bfb4"]
}, Open  ]],
Cell[CellGroupData[{
Cell[94941, 2868, 215, 4, 30, "Input",ExpressionUUID->"e0f54638-75a1-449a-9841-76f7cb67e3ec"],
Cell[95159, 2874, 1478, 42, 70, "Output",ExpressionUUID->"2e731fc5-1609-4e0b-b1f6-8643f9f27d7a"]
}, Open  ]],
Cell[CellGroupData[{
Cell[96674, 2921, 214, 4, 30, "Input",ExpressionUUID->"12fbe844-c489-4b64-8575-1f665d7297c0"],
Cell[96891, 2927, 6428, 245, 70, "Output",ExpressionUUID->"2d87cdc9-e0ce-4d51-873a-b04739110d14"]
}, Open  ]],
Cell[CellGroupData[{
Cell[103356, 3177, 213, 4, 30, "Input",ExpressionUUID->"8b813d86-442c-4591-85d8-9a09b379c4bf"],
Cell[103572, 3183, 7402, 277, 70, "Output",ExpressionUUID->"afaecca2-8d0a-4b77-a15e-135faec92ada"]
}, Open  ]],
Cell[CellGroupData[{
Cell[111011, 3465, 214, 4, 30, "Input",ExpressionUUID->"cc593f67-7c38-4503-9d2b-686d309c0ec9"],
Cell[111228, 3471, 8530, 316, 70, "Output",ExpressionUUID->"2dae6e61-238f-4056-ad67-45423292f3f0"]
}, Open  ]],
Cell[CellGroupData[{
Cell[119795, 3792, 211, 4, 30, "Input",ExpressionUUID->"f17e7103-1581-4aaf-bd1a-e01267da1173"],
Cell[120009, 3798, 5676, 218, 70, "Output",ExpressionUUID->"545d3f5c-897e-4b1d-9bae-e726170cf7d9"]
}, Open  ]],
Cell[CellGroupData[{
Cell[125722, 4021, 214, 4, 30, "Input",ExpressionUUID->"2cab1fe6-d0ab-46ad-8359-2ca694428425"],
Cell[125939, 4027, 6301, 238, 70, "Output",ExpressionUUID->"42757452-d4a4-40fb-adf8-7e0907df8c69"]
}, Open  ]],
Cell[CellGroupData[{
Cell[132277, 4270, 213, 4, 30, "Input",ExpressionUUID->"0fe01854-b506-4936-a55c-53b2b51d4c8f"],
Cell[132493, 4276, 4915, 183, 70, "Output",ExpressionUUID->"7d09ec4f-ea27-46aa-8dd3-c324dc0b8ae2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[137445, 4464, 214, 4, 30, "Input",ExpressionUUID->"60ec46e5-58cf-4517-8cb1-fe5ef63fb2b0"],
Cell[137662, 4470, 6355, 240, 70, "Output",ExpressionUUID->"fd8c1e92-c463-48c7-a597-3374896a8c5e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[144054, 4715, 214, 4, 30, "Input",ExpressionUUID->"b3df6f7a-92ad-4567-84b7-118ec92a22d5"],
Cell[144271, 4721, 9335, 340, 70, "Output",ExpressionUUID->"298d89ae-b74f-4e60-8afc-e9618ab28404"]
}, Open  ]],
Cell[CellGroupData[{
Cell[153643, 5066, 216, 4, 30, "Input",ExpressionUUID->"83bd893f-c7a1-4c62-8c6d-7ece882728f7"],
Cell[153862, 5072, 5166, 190, 70, "Output",ExpressionUUID->"299f6d33-f7e9-4932-be1c-8645536f9635"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[159077, 5268, 388, 8, 38, "Subsection",ExpressionUUID->"6b9af708-aca5-4ed2-9649-67f8f4ad392a"],
Cell[CellGroupData[{
Cell[159490, 5280, 794, 16, 52, "Input",ExpressionUUID->"e81fec8d-ea79-4cd7-b698-0ad442fbf35d"],
Cell[160287, 5298, 6647, 240, 70, "Output",ExpressionUUID->"b858e4de-2f6d-425f-a3c5-0069af32ade4"]
}, Open  ]],
Cell[CellGroupData[{
Cell[166971, 5543, 242, 5, 30, "Input",ExpressionUUID->"79f97ed2-67d2-4bf8-aef2-f0352c6677e3"],
Cell[167216, 5550, 414, 8, 70, "Output",ExpressionUUID->"13c88d6e-f2e3-40c6-8720-82bdc0959158"]
}, Open  ]],
Cell[CellGroupData[{
Cell[167667, 5563, 337, 7, 52, "Input",ExpressionUUID->"0b25b621-273b-434a-9a8b-2e218eb44822"],
Cell[168007, 5572, 4801, 164, 70, "Output",ExpressionUUID->"8fd7f63d-058d-4a51-b326-886b1106286b"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[172857, 5742, 473, 7, 38, "Subsection",ExpressionUUID->"2c356fc7-7d65-4c10-8843-f074cd1d1693"],
Cell[CellGroupData[{
Cell[173355, 5753, 654, 11, 52, "Input",ExpressionUUID->"3cbda2eb-c6ef-4f25-bd5b-45be63516047"],
Cell[174012, 5766, 642, 10, 34, "Output",ExpressionUUID->"742e49e7-b82f-4a4a-8fe0-f18c468bdb90"],
Cell[174657, 5778, 713, 13, 34, "Output",ExpressionUUID->"a0f15a31-e27f-481a-b166-1b4874c6f03f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[175407, 5796, 418, 8, 52, "Input",ExpressionUUID->"1c60e7f5-a6f9-4d1e-87c3-ecaccf925aa5"],
Cell[175828, 5806, 372, 7, 34, "Output",ExpressionUUID->"e0be12ec-29b1-4714-b204-ed6aad44e0f6"],
Cell[176203, 5815, 515, 13, 34, "Output",ExpressionUUID->"253c6d1e-cec1-449f-9ab1-ce6d9b556975"]
}, Open  ]]
}, Closed]]
}, Open  ]]
}
]
*)

